Take-Home Exercise 2: Applied Spatial Interaction Models - A Case Study of Singapore Public Bus Commuter Flows

Author

Goh Si Hui

Published

December 8, 2023

Modified

December 16, 2023

1 Overview

1.1 Introduction

What are the driving forces behind urban dwellers to weak up early in morning to commute from their home locations to their work places? What are the impact of removing a public bus service on the commuters reside along the corridor of the bus route? These are some questions faced by transport operators and urban managers.

To answer these many questions related to urban mobility, traditionally commuters survey would be used. However, conducting commuters survey is costly, time-consuming and laborious. In addition, survey data tend to take a long time to clean and analyse, which can lead to the collected information being out-of-date when the survey report was ready.

With the recent trend of massive deployment of pervasive computing technologies such as GPS on the vehicles and SMART cards used by public transport commuters, we will utilise and transform geospatially-referenced data into insightful information, hence generating returns on the investment made to collect and manage this data.

1.2 Objectives

In this take-home exercise, we will be using publicly available data and geospatial data science and analysis to answer questions related to urban mobility and how it can be used to support decision-making. In particular, we will be building spatial interaction models to determine factors affecting urban mobility patterns of public bus transit.

1.3 Packages Used

For this exercise, we will be using the following packages:

  • sf : to import, integrate, process and transform geospatial data

  • sp: to provide classes and methods for spatial data types

  • DT:to display R data objects (matrices or dataframes) as tables on HTML pages

  • stplanr: to visualise flow lines

  • performance:to compute measures for assessing model quality

  • reshape2:to restructure and aggregate data

  • tidyverse: to import, integrate, wrangle and visualise data

  • tmap: to create thematic maps

  • ggpubr: to create and customise ‘ggplot2’- based publication ready plots

Show the code
pacman::p_load(tmap, sf, sp, DT, stplanr, performance, reshape2, ggpubr, tidyverse) 

2 Data Preparation

For the purpose of this take-home exercise, we will be using the following datasets downloaded from LTA Datamall, Data.gov.sg and datasets provided by the course instructor.

  • Geospatial Data

    • Bus Stop Location

    • Train Station Exit Point

    • Master Plan 2019 Subzone Boundary

    • Business,

    • FinServ,

  • Aspatial Data

    • Passenger Volume by Origin Destination Bus Stops

    • hdb: contains the location of existing HDB blocks, highest floor, year of completion, type of building and number of HDB flats, total dwelling units, numer of flats sold by flat type

    • schools

2.1 Importing Data into R

odbus <- read_csv("data/aspatial/origin_destination_bus_202310.csv")
hdb <- read_csv("data/aspatial/hdb.csv")
schools <- read_csv("data/aspatial/schools1.csv")
busstop <- st_read(dsn = "data/geospatial",
                   layer = "BusStop")
Reading layer `BusStop' from data source 
  `C:\sihuihui\ISSS624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 5161 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21
mpsz <- st_read(dsn = "data/geospatial",
                   layer = "MPSZ-2019")
Reading layer `MPSZ-2019' from data source 
  `C:\sihuihui\ISSS624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84
business <- st_read(dsn = "data/geospatial",
                   layer = "Business")
Reading layer `Business' from data source 
  `C:\sihuihui\ISSS624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 6550 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3669.148 ymin: 25408.41 xmax: 47034.83 ymax: 50148.54
Projected CRS: SVY21 / Singapore TM
finserv <- st_read(dsn = "data/geospatial",
                   layer = "FinServ")
Reading layer `FinServ' from data source 
  `C:\sihuihui\ISSS624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 3320 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 4881.527 ymin: 25171.88 xmax: 46526.16 ymax: 49338.02
Projected CRS: SVY21 / Singapore TM
mrtexits <- st_read(dsn = "data/geospatial",
                   layer = "Train_Station_Exit_Layer")
Reading layer `Train_Station_Exit_Layer' from data source 
  `C:\sihuihui\ISSS624\Take-home_Ex\Take-home_Ex2\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 565 features and 2 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 6134.086 ymin: 27499.7 xmax: 45356.36 ymax: 47865.92
Projected CRS: SVY21

2.2 Data Wrangling of Aspatial Data

2.2.1 Passenger Volumes from Origin Busstops

Show the code
glimpse(odbus)
Rows: 5,694,297
Columns: 7
$ YEAR_MONTH          <chr> "2023-10", "2023-10", "2023-10", "2023-10", "2023-…
$ DAY_TYPE            <chr> "WEEKENDS/HOLIDAY", "WEEKDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR       <dbl> 16, 16, 14, 14, 17, 17, 17, 7, 14, 14, 10, 20, 20,…
$ PT_TYPE             <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE      <chr> "04168", "04168", "80119", "80119", "44069", "2028…
$ DESTINATION_PT_CODE <chr> "10051", "10051", "90079", "90079", "17229", "2014…
$ TOTAL_TRIPS         <dbl> 3, 5, 3, 5, 4, 1, 24, 2, 1, 7, 3, 2, 5, 1, 1, 1, 1…

From the above output, it shows that the values of the ORIGIN_PT_CODE and DESTINATION_PT_CODE are in character data type. Since these two columns contain the origin bus stop codes and destination bus stop codes and they actually take on a limited number of different values (unlike strings), we convert ORIGIN_PT_CODE and DESTINATION_PT_CODE into factor data type using as.factor().

Show the code
odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE)

Let us check the odbus dataframe using glimpse() again.

Show the code
glimpse(odbus)
Rows: 5,694,297
Columns: 7
$ YEAR_MONTH          <chr> "2023-10", "2023-10", "2023-10", "2023-10", "2023-…
$ DAY_TYPE            <chr> "WEEKENDS/HOLIDAY", "WEEKDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR       <dbl> 16, 16, 14, 14, 17, 17, 17, 7, 14, 14, 10, 20, 20,…
$ PT_TYPE             <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE      <fct> 04168, 04168, 80119, 80119, 44069, 20281, 20281, 1…
$ DESTINATION_PT_CODE <fct> 10051, 10051, 90079, 90079, 17229, 20141, 20141, 1…
$ TOTAL_TRIPS         <dbl> 3, 5, 3, 5, 4, 1, 24, 2, 1, 7, 3, 2, 5, 1, 1, 1, 1…

ORIGIN_PT_CODE and DESTINATION_PT_CODE have been converted to factor data type.

Next, we will do a check on the data. Using unique() function, we can find the unique values in a column. Let us first check the YEAR_MONTH, DAY_TYPE, TIME_PER_HOUR and PT_TYPE to ensure the data contains bus trips made in October 2023, and there are no other unexpected values for DAY_TYPE and TIME_PER_HOUR.

unique(odbus$YEAR_MONTH)
[1] "2023-10"
unique(odbus$DAY_TYPE)
[1] "WEEKENDS/HOLIDAY" "WEEKDAY"         
unique(odbus$TIME_PER_HOUR)
 [1] 16 14 17  7 10 20 19  5 11  8 21 18  9  6 12 15 23 13 22  0  1  4  2
#To count the number hours listed
length(unique(odbus$TIME_PER_HOUR))
[1] 23
unique(odbus$PT_TYPE)
[1] "BUS"

From the above output, we know that the data only contains bus trips made in October 2023. The DAY_TYPES have 2 categories: WEEKDAYS and WEEKENDS/HOLIDAY. TIME_PER_HOUR have 23 categories because there is no value of “3” in TIME_PER_HOUR variable.

2.2.2 Extract the time period we are interested in - Weekday Morning Peak Hour

For the purpose of this exercise, we are interested in the bus commuter flows on weekdays morning peak hour (i.e. 6am to 9am) so we will use the following code chunk to extract the time period we are interested in and save the output in rds format for future use.

Show the code
odbus_WDMP <- odbus %>%
  filter(DAY_TYPE == "WEEKDAY") %>%
  filter(TIME_PER_HOUR >= 6 &
           TIME_PER_HOUR <= 9) %>%
  group_by(ORIGIN_PT_CODE, 
           DESTINATION_PT_CODE) %>%
  summarise(TRIPS = sum(TOTAL_TRIPS))

Let us check the extracted passenger volume from origin busstops on weekday morning peak hour.

summary(odbus_WDMP)
 ORIGIN_PT_CODE   DESTINATION_PT_CODE     TRIPS        
 22009  :   582   22009  :   584      Min.   :    1.0  
 84009  :   562   52009  :   554      1st Qu.:    3.0  
 75009  :   554   75009  :   535      Median :   15.0  
 52009  :   548   84009  :   533      Mean   :  107.2  
 59009  :   466   03129  :   474      3rd Qu.:   57.0  
 46009  :   458   59009  :   466      Max.   :97600.0  
 (Other):239038   (Other):239062                       

We will use the following code chunk to save this dataframe in rds format for future use.

write_rds(odbus_WDMP, "data/rds/odbus_WDMP.rds")

2.2.3 HDB Data

We will now take a look at the HDB data.

Show the code
glimpse(hdb)
Rows: 12,442
Columns: 37
$ ...1                  <dbl> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14…
$ blk_no                <chr> "1", "1", "1", "1", "1", "1", "1", "1", "1", "1"…
$ street                <chr> "BEACH RD", "BEDOK STH AVE 1", "CANTONMENT RD", …
$ max_floor_lvl         <dbl> 16, 14, 2, 15, 4, 25, 12, 14, 12, 2, 15, 15, 13,…
$ year_completed        <dbl> 1970, 1975, 2010, 1982, 1975, 1982, 1975, 1977, …
$ residential           <chr> "Y", "Y", "N", "Y", "Y", "Y", "Y", "Y", "Y", "N"…
$ commercial            <chr> "Y", "N", "Y", "N", "Y", "N", "N", "N", "Y", "Y"…
$ market_hawker         <chr> "N", "N", "N", "N", "N", "N", "N", "N", "N", "N"…
$ miscellaneous         <chr> "N", "Y", "N", "N", "N", "N", "Y", "Y", "N", "N"…
$ multistorey_carpark   <chr> "N", "N", "N", "N", "N", "N", "N", "N", "N", "N"…
$ precinct_pavilion     <chr> "N", "N", "N", "N", "N", "N", "N", "N", "N", "N"…
$ bldg_contract_town    <chr> "KWN", "BD", "CT", "BD", "PRC", "BM", "QT", "GL"…
$ total_dwelling_units  <dbl> 142, 206, 0, 102, 55, 96, 125, 247, 95, 0, 220, …
$ `1room_sold`          <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ `2room_sold`          <dbl> 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ `3room_sold`          <dbl> 138, 204, 0, 0, 54, 0, 118, 0, 62, 0, 216, 214, …
$ `4room_sold`          <dbl> 1, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ `5room_sold`          <dbl> 2, 2, 0, 92, 1, 96, 7, 0, 33, 0, 4, 5, 0, 4, 0, …
$ exec_sold             <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ multigen_sold         <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ studio_apartment_sold <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ `1room_rental`        <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 319, 0, 0, 0…
$ `2room_rental`        <dbl> 0, 0, 0, 0, 0, 0, 0, 247, 0, 0, 0, 0, 0, 0, 56, …
$ `3room_rental`        <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 1,…
$ other_room_rental     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0,…
$ lat                   <dbl> 1.295097, 1.320852, 1.275488, 1.327969, 1.388610…
$ lng                   <dbl> 103.8541, 103.9337, 103.8414, 103.9227, 103.9881…
$ building              <chr> "RAFFLES HOTEL", "NIL", "PINNACLE @ DUXTON", "PI…
$ addr                  <chr> "1 BEACH ROAD RAFFLES HOTEL SINGAPORE 189673", "…
$ postal                <chr> "189673", "460001", "080001", "461001", "500001"…
$ SUBZONE_NO            <dbl> 2, 6, 3, 3, 1, 9, 10, 5, 3, 5, 1, 5, 2, 2, 1, 7,…
$ SUBZONE_N             <chr> "CITY HALL", "BEDOK SOUTH", "CHINATOWN", "KEMBAN…
$ SUBZONE_C             <chr> "DTSZ02", "BDSZ06", "OTSZ03", "BDSZ03", "CHSZ01"…
$ PLN_AREA_N            <chr> "DOWNTOWN CORE", "BEDOK", "OUTRAM", "BEDOK", "CH…
$ PLN_AREA_C            <chr> "DT", "BD", "OT", "BD", "CH", "BM", "QT", "GL", …
$ REGION_N              <chr> "CENTRAL REGION", "EAST REGION", "CENTRAL REGION…
$ REGION_C              <chr> "CR", "ER", "CR", "ER", "ER", "CR", "CR", "CR", …

From the above output, we know that there are some HDB buildings considered as residential, commercial, market, pavillion and even carparks. We will filter the residential and commercial HDB buildings out and save them as different dataframes because these could be propulsive or attractive factors for people to travel in morning peak hour (e.g. people would want to move away from residential areas and move towards commercial buildings in the morning for work).

hdb_residential <- hdb %>%
  filter(residential == "Y") %>%
  select(postal, lat, lng, SUBZONE_N, residential, total_dwelling_units)
glimpse(hdb_residential)
Rows: 10,181
Columns: 6
$ postal               <chr> "189673", "460001", "461001", "500001", "160001",…
$ lat                  <dbl> 1.295097, 1.320852, 1.327969, 1.388610, 1.292075,…
$ lng                  <dbl> 103.8541, 103.9337, 103.9227, 103.9881, 103.8286,…
$ SUBZONE_N            <chr> "CITY HALL", "BEDOK SOUTH", "KEMBANGAN", "CHANGI …
$ residential          <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y",…
$ total_dwelling_units <dbl> 142, 206, 102, 55, 96, 125, 247, 95, 220, 219, 31…

We check if there are any duplicates in the hdb_residential dataset using the following code chunk.

Show the code
duplicate <- hdb_residential %>%
  group_by_all() %>% 
  filter(n()>1) %>%
  ungroup()

duplicate
# A tibble: 0 × 6
# ℹ 6 variables: postal <chr>, lat <dbl>, lng <dbl>, SUBZONE_N <chr>,
#   residential <chr>, total_dwelling_units <dbl>

From the above output, we know that there is no duplicate rows in the hdb_residential dataframe.

We will now extract the data for HDB Commercial Buildings.

hdb_commercial <- hdb %>%
  filter(commercial == "Y") %>%
  select(postal, lat, lng, SUBZONE_N, commercial, total_dwelling_units)
glimpse(hdb_commercial)
Rows: 2,508
Columns: 6
$ postal               <chr> "189673", "080001", "500001", "080001", "408528",…
$ lat                  <dbl> 1.295097, 1.275488, 1.388610, 1.275499, 1.316494,…
$ lng                  <dbl> 103.8541, 103.8414, 103.9881, 103.8414, 103.8968,…
$ SUBZONE_N            <chr> "CITY HALL", "CHINATOWN", "CHANGI POINT", "CHINAT…
$ commercial           <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y",…
$ total_dwelling_units <dbl> 142, 0, 55, 95, 0, 244, 0, 96, 176, 148, 163, 8, …

We check if there are any duplicates in the hdb_commercial dataset using the following code chunk.

Show the code
duplicate1 <- hdb_commercial %>%
  group_by_all() %>% 
  filter(n()>1) %>%
  ungroup()

duplicate1
# A tibble: 0 × 6
# ℹ 6 variables: postal <chr>, lat <dbl>, lng <dbl>, SUBZONE_N <chr>,
#   commercial <chr>, total_dwelling_units <dbl>

From the output we see that there are no duplicates.

Let us check further to see if there are any buildings with same postal code but occupy 2 different longitude and latitude.

Show the code
same_postal <- hdb_commercial %>%
  group_by(postal) %>% 
  filter(n()>1) %>%
  ungroup()

same_postal
# A tibble: 43 × 6
   postal   lat   lng SUBZONE_N        commercial total_dwelling_units
   <chr>  <dbl> <dbl> <chr>            <chr>                     <dbl>
 1 080001  1.28  104. CHINATOWN        Y                             0
 2 080001  1.28  104. CHINATOWN        Y                            95
 3 NIL     1.34  104. TOA PAYOH WEST   Y                           200
 4 NIL     1.28  104. TIONG BAHRU      Y                           113
 5 NIL     1.34  104. TOA PAYOH WEST   Y                             0
 6 NIL     1.33  104. POTONG PASIR     Y                             0
 7 NIL     1.30  104. BUGIS            Y                            76
 8 NIL     1.37  104. SERANGOON GARDEN Y                            89
 9 NIL     1.35  104. BUKIT BATOK WEST Y                            17
10 NIL     1.32  104. BEDOK SOUTH      Y                            16
# ℹ 33 more rows

From the output, we find that there are postal code 080001 occupies 2 different geographical locations and one location has no commercial dwellings while another location has 95 dwelling units. For this analysis, since we are going to analyse the commuter flows at the analytical hexagon level, I choose to retain these 2 geographical location despite them sharing the same postal code. This is because (1) they could end up in 2 different hexagon grids and (2) removing 1 and not the other could cause us to misinterpret the information. For the remaining rows, they are different geographical locations but do not have a postal code. I choose to retain these geographical locations despite them not having postal code because we will be using their latitude and longitude in the subsequent steps to convert it into a simple feature data frame and they will give us the point geometry point coordinates.

2.2.4 Schools Information

We will now take a look at the imported schools data.

Show the code
glimpse(schools)
Rows: 350
Columns: 41
$ ...1               <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, …
$ postal_code        <chr> "088256", "099138", "099757", "099840", "109100", "…
$ school_name        <chr> "CANTONMENT PRIMARY SCHOOL", "CHIJ ST. THERESA'S CO…
$ url_address        <chr> "http://www.cantonmentpri.moe.edu.sg", "http://www.…
$ address            <chr> "1    Cantonment Close", "160  LOWER DELTA ROAD", "…
$ telephone_no       <chr> "65119555", "64775777", "62730096", "62733937", "62…
$ telephone_no_2     <chr> "na", "na", "na", "na", "na", "na", "na", "na", "na…
$ fax_no             <chr> "65119556", "64775700", "62731710", "62763083", "62…
$ fax_no_2           <chr> "na", "na", "na", "na", "na", "na", "na", "na", "na…
$ email_address      <chr> "cantonment_ps@moe.edu.sg", "CHIJSTCS@MOE.EDU.SG", …
$ mrt_desc           <chr> "Tanjong Pagar Outram Park", "HARBOURFRONT MRT, TIO…
$ bus_desc           <chr> "75, 167, 196", "65, 121, 123, 123M, 124, 131, 131M…
$ principal_name     <chr> "MRS MANOKARA SUGUNAVATHI", "MDM TAN MEI MEI JENNY"…
$ first_vp_name      <chr> "MRS AUDREA CHIN", "MDM ONG LEE LEE", "MS NG CHIOU …
$ second_vp_name     <chr> "MISS CHENG SHIN MIIN", "MISS KUO ZHAOYAN, FELICIA"…
$ third_vp_name      <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ fourth_vp_name     <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ fifth_vp_name      <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ sixth_vp_name      <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ dgp_code           <chr> "BUKIT MERAH", "BUKIT MERAH", "BUKIT MERAH", "BUKIT…
$ zone_code          <chr> "SOUTH", "SOUTH", "SOUTH", "SOUTH", "SOUTH", "SOUTH…
$ type_code          <chr> "GOVERNMENT SCHOOL", "GOVERNMENT-AIDED SCH", "GOVER…
$ nature_code        <chr> "CO-ED SCHOOL", "GIRLS' SCHOOL", "GIRLS' SCHOOL", "…
$ session_code       <chr> "SINGLE SESSION", "SINGLE SESSION", "SINGLE SESSION…
$ mainlevel_code     <chr> "PRIMARY", "SECONDARY", "PRIMARY", "PRIMARY", "PRIM…
$ sap_ind            <chr> "No", "No", "No", "No", "No", "No", "No", "No", "Ye…
$ autonomous_ind     <chr> "No", "No", "No", "No", "No", "No", "No", "No", "No…
$ gifted_ind         <chr> "No", "No", "No", "No", "No", "No", "No", "No", "Ye…
$ ip_ind             <chr> "No", "No", "No", "No", "No", "No", "No", "No", "No…
$ mothertongue1_code <chr> "Chinese", "Chinese", "Chinese", "Chinese", "Chines…
$ mothertongue2_code <chr> "Malay", "Malay", "Malay", "Malay", "Malay", "Malay…
$ mothertongue3_code <chr> "Tamil", "Tamil", "Tamil", "Tamil", "Tamil", "na", …
$ results.SEARCHVAL  <chr> "KIDZ TREEHOUSE @ CANTONMENT", "CHIJ SAINT THERESA'…
$ results.BLK_NO     <chr> "1", "160", "1", "1", "91", "147", "301", "50", "30…
$ results.ROAD_NAME  <chr> "CANTONMENT CLOSE", "LOWER DELTA ROAD", "BUKIT TERE…
$ results.BUILDING   <chr> "KIDZ TREEHOUSE @ CANTONMENT", "CHIJ SAINT THERESA'…
$ results.ADDRESS    <chr> "1 CANTONMENT CLOSE KIDZ TREEHOUSE @ CANTONMENT SIN…
$ results.X          <dbl> 28748.16, 26789.38, 27402.97, 26983.87, 25248.37, 2…
$ results.Y          <dbl> 28660.00, 28647.44, 28579.85, 28603.93, 28733.28, 3…
$ results.LATITUDE   <dbl> 1.275465, 1.275352, 1.274740, 1.274958, 1.276128, 1…
$ results.LONGITUDE  <dbl> 103.8400, 103.8224, 103.8280, 103.8242, 103.8086, 1…

There are a lot of information that we do not need from the imported data (e.g. School principal) so we will use the following code chunk to retain the columns that we want and also rename the results.LATITUDE and results.LONGITUDE columns to latitude and longitude respectively.

schools_tidy <- schools %>%
  rename(latitude = "results.LATITUDE",
         longitude = "results.LONGITUDE")%>%
  select(postal_code, school_name, latitude, longitude)
glimpse(schools_tidy)
Rows: 350
Columns: 4
$ postal_code <chr> "088256", "099138", "099757", "099840", "109100", "127368"…
$ school_name <chr> "CANTONMENT PRIMARY SCHOOL", "CHIJ ST. THERESA'S CONVENT",…
$ latitude    <dbl> 1.275465, 1.275352, 1.274740, 1.274958, 1.276128, 1.301228…
$ longitude   <dbl> 103.8400, 103.8224, 103.8280, 103.8242, 103.8086, 103.7649…

We will now check if there are any duplicates in the schools_tidy data frame.

Show the code
duplicate2 <- schools_tidy %>%
  group_by_all() %>% 
  filter(n()>1) %>%
  ungroup()

duplicate2
# A tibble: 8 × 4
  postal_code school_name                             latitude longitude
  <chr>       <chr>                                      <dbl>     <dbl>
1 309437      SINGAPORE CHINESE GIRLS' PRIMARY SCHOOL     1.32      104.
2 309437      SINGAPORE CHINESE GIRLS' PRIMARY SCHOOL     1.32      104.
3 309437      SINGAPORE CHINESE GIRLS' SCHOOL             1.32      104.
4 309437      SINGAPORE CHINESE GIRLS' SCHOOL             1.32      104.
5 599986      METHODIST GIRLS' SCHOOL (SECONDARY)         1.33      104.
6 599986      METHODIST GIRLS' SCHOOL (SECONDARY)         1.33      104.
7 599986      METHODIST GIRLS' SCHOOL (PRIMARY)           1.33      104.
8 599986      METHODIST GIRLS' SCHOOL (PRIMARY)           1.33      104.

From the above output, we find that there are duplicate entries for Singapore Chinese Girls’ Primary School, Singapore Chinese Girls’ School, Methodist Girls’ School (Secondary) and Methodist Girls’ School (Primary). Hence we will remove the duplicates using the following code chunk.

Show the code
schools_tidy <- unique(schools_tidy)

Let us do a check to confirm that there are no duplicates in the data frame now.

Show the code
duplicate3 <- schools_tidy %>%
  group_by_all() %>% 
  filter(n()>1) %>%
  ungroup()

duplicate3
# A tibble: 0 × 4
# ℹ 4 variables: postal_code <chr>, school_name <chr>, latitude <dbl>,
#   longitude <dbl>

From the above output, it shows that there are no more duplicates in the dataframe.

2.2.5 Converting Aspatial data into SF Tibble Dataframe

Currently the hdb residential, hdb commercial and school_tidy data are still asaptial data even though they have latitude and longitude information. So we will use st_as_sf() to convert it into an sf tibble dataframe and use st_transform() to change it to SYV21 projected coordinate system (i.e. the crs code is 3414)

We use the following code chunk to convert hdb residential data into an sf tibble dataframe.

hdb_residental_sf <- st_as_sf(hdb_residential, 
                              coords = c("lng", "lat"),
                              crs=4326) %>%
  st_transform(crs = 3414)
glimpse(hdb_residental_sf)
Rows: 10,181
Columns: 5
$ postal               <chr> "189673", "460001", "461001", "500001", "160001",…
$ SUBZONE_N            <chr> "CITY HALL", "BEDOK SOUTH", "KEMBANGAN", "CHANGI …
$ residential          <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y",…
$ total_dwelling_units <dbl> 142, 206, 102, 55, 96, 125, 247, 95, 220, 219, 31…
$ geometry             <POINT [m]> POINT (30309.27 30830.82), POINT (39173.81 …

We use the following code chunk to convert hdb commercial data into an sf tibble dataframe.

hdb_commercial_sf <- st_as_sf(hdb_commercial, 
                              coords = c("lng", "lat"),
                              crs=4326) %>%
  st_transform(crs = 3414)
glimpse(hdb_commercial_sf)
Rows: 2,508
Columns: 5
$ postal               <chr> "189673", "080001", "500001", "080001", "408528",…
$ SUBZONE_N            <chr> "CITY HALL", "CHINATOWN", "CHANGI POINT", "CHINAT…
$ commercial           <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y",…
$ total_dwelling_units <dbl> 142, 0, 55, 95, 0, 244, 0, 96, 176, 148, 163, 8, …
$ geometry             <POINT [m]> POINT (30309.27 30830.82), POINT (28901.52 …

We use the following code chunk to convert schools_tidy into an sf tibble dataframe.

schools_sf <- st_as_sf(schools_tidy,
                       coords = c("longitude", "latitude"), 
                       crs=4326) %>%
  st_transform(crs=3414)
glimpse(schools_sf)
Rows: 346
Columns: 3
$ postal_code <chr> "088256", "099138", "099757", "099840", "109100", "127368"…
$ school_name <chr> "CANTONMENT PRIMARY SCHOOL", "CHIJ ST. THERESA'S CONVENT",…
$ geometry    <POINT [m]> POINT (28748.16 28660), POINT (26789.38 28647.44), P…

2.3 Data Wrangling of Spatial Data

We will now take a look at the spatial data imported in.

glimpse(mpsz)
Rows: 332
Columns: 7
$ SUBZONE_N  <chr> "MARINA EAST", "INSTITUTION HILL", "ROBERTSON QUAY", "JURON…
$ SUBZONE_C  <chr> "MESZ01", "RVSZ05", "SRSZ01", "WISZ01", "MUSZ02", "MPSZ05",…
$ PLN_AREA_N <chr> "MARINA EAST", "RIVER VALLEY", "SINGAPORE RIVER", "WESTERN …
$ PLN_AREA_C <chr> "ME", "RV", "SR", "WI", "MU", "MP", "WI", "WI", "SI", "SI",…
$ REGION_N   <chr> "CENTRAL REGION", "CENTRAL REGION", "CENTRAL REGION", "WEST…
$ REGION_C   <chr> "CR", "CR", "CR", "WR", "CR", "CR", "WR", "WR", "CR", "CR",…
$ geometry   <MULTIPOLYGON [°]> MULTIPOLYGON (((103.8802 1...., MULTIPOLYGON (…
glimpse(busstop)
Rows: 5,161
Columns: 4
$ BUS_STOP_N <chr> "22069", "32071", "44331", "96081", "11561", "66191", "2338…
$ BUS_ROOF_N <chr> "B06", "B23", "B01", "B05", "B05", "B03", "B02A", "B02", "B…
$ LOC_DESC   <chr> "OPP CEVA LOGISTICS", "AFT TRACK 13", "BLK 239", "GRACE IND…
$ geometry   <POINT [m]> POINT (13576.31 32883.65), POINT (13228.59 44206.38),…
glimpse(mrtexits)
Rows: 565
Columns: 3
$ stn_name  <chr> "MACPHERSON MRT STATION", "MACPHERSON MRT STATION", "MACPHER…
$ exit_code <chr> "Exit A", "Exit B", "Exit C", "Exit B", "Exit A", "Exit A", …
$ geometry  <POINT [m]> POINT (34285.07 34322.99), POINT (34382.15 34231.9), P…
glimpse(business)
Rows: 6,550
Columns: 4
$ POI_NAME   <chr> "JOHN CHEN", "TROPICAL INDUSTRIAL BUILDING", "LIAN CHEONG I…
$ POI_ST_NUM <chr> "6", "14", "12", NA, "2", "21", "68", "68", NA, "14", "10",…
$ POI_ST_NAM <chr> "LITTLE RD", "LITTLE RD", "LITTLE RD", NA, "LITTLE RD", "LO…
$ geometry   <POINT [m]> POINT (33818.36 35620.16), POINT (33770.51 35610.2), …
glimpse(finserv)
Rows: 3,320
Columns: 4
$ POI_NAME   <chr> "UOB", "POSB", "UOB", "OCBC", "OCBC", "MAYBANK", "ADPOST MO…
$ POI_ST_NUM <chr> "201", "375", "375", "375", NA, "707", "163", NA, "11", NA,…
$ POI_ST_NAM <chr> "YISHUN AVE 2", "COMMONWEALTH AVE", "COMMONWEALTH AVE", "CO…
$ geometry   <POINT [m]> POINT (27966.77 44304.65), POINT (24163.96 31606.25),…

We noticed that mpsz dataset is made up of multipolygons while the remaining datasets are made up of point geometry.

Let us now check the coordinates system using the st_crs() function.

st_crs(mpsz)
Coordinate Reference System:
  User input: WGS 84 
  wkt:
GEOGCRS["WGS 84",
    DATUM["World Geodetic System 1984",
        ELLIPSOID["WGS 84",6378137,298.257223563,
            LENGTHUNIT["metre",1]]],
    PRIMEM["Greenwich",0,
        ANGLEUNIT["degree",0.0174532925199433]],
    CS[ellipsoidal,2],
        AXIS["latitude",north,
            ORDER[1],
            ANGLEUNIT["degree",0.0174532925199433]],
        AXIS["longitude",east,
            ORDER[2],
            ANGLEUNIT["degree",0.0174532925199433]],
    ID["EPSG",4326]]
st_crs(busstop)
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["WGS 84",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]
st_crs(mrtexits)
Coordinate Reference System:
  User input: SVY21 
  wkt:
PROJCRS["SVY21",
    BASEGEOGCRS["WGS 84",
        DATUM["World Geodetic System 1984",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]],
            ID["EPSG",6326]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["unnamed",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1,
                ID["EPSG",9001]]]]
st_crs(business)
Coordinate Reference System:
  User input: SVY21 / Singapore TM 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
st_crs(finserv)
Coordinate Reference System:
  User input: SVY21 / Singapore TM 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

From the above output, we see that the coordinate system for mpsz is WGS 84, and the coorinate systems for the remaining datasets are SVY21. However, busstop and trainexits still have ‘9001’ in the output of st_crs(), meaning that this is a wrong EPSG code because the correct EPSG code for SVY21 should be 3414.

We use st_transform transform the CRS for mpsz because it was in another projection format. Then we use st_set_crs() to assign the correct ESPG code to the various sf dataframe.

mpsz3414 <- st_transform(mpsz, crs=3414)
st_crs(mpsz3414)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
busstop3414 <- st_set_crs(busstop, 3414)
st_crs(busstop3414)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
mrtexits3414 <- st_set_crs(mrtexits, 3414)
st_crs(mrtexits3414)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
business3414 <- st_set_crs(business, 3414)
st_crs(business3414)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
finserv3414 <- st_set_crs(finserv, 3414)
st_crs(finserv3414)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

2.3.1 Creating the Analytical Hexagon Layer

For this exercise, we will be analysing the bus commuter flows at analytics hexagon level. The analytical hexagon data is 375m between the centre of the hexagon and its edges to represent the traffic analysis zone.

First, we will create a hexagon tessellation using MPSZ3414 to define the bounding box of the tessellation. As the hexagon layer that we want is 375m (the perpendicular distance between the centre of the hexagon and its edge), and the cellsize parameter in st_make_grid() requires the length to be between opposite edges, we multiply 375m by 2 to get 750m, which is the distance between 2 opposite edges of a hexagon.

In the code chunk below, we also specify the crs = 3414 since we are using the SVY21 coordinate reference system and set square = FALSE to return a hexagon grid (rather than a square grid).

Show the code
hex_grid <- st_make_grid(mpsz3414, c(750,750), crs= 3414, what = "polygons", square = FALSE)

head(hex_grid, 10)
Geometry set for 10 features 
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 1917.538 ymin: 15965.23 xmax: 2667.538 ymax: 28522.6
Projected CRS: SVY21 / Singapore TM
First 5 geometries:

Next, we convert hex_grid from a sfc_POLYGON object to sf object for easier handling and add an unique ID to each cell. Each cell is a hexagon and in subsequent steps, we will check the number of trips, count the number of businesses, financial services, schools, residential units, hdb commercial units within each hexagon.

Show the code
hex_grid_sf <- st_sf(hex_grid) %>%
  mutate(grid_id = 1:length(lengths(hex_grid)))

head(hex_grid_sf, 10)
Simple feature collection with 10 features and 1 field
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 1917.538 ymin: 15965.23 xmax: 2667.538 ymax: 28522.6
Projected CRS: SVY21 / Singapore TM
                         hex_grid grid_id
1  POLYGON ((2292.538 15965.23...       1
2  POLYGON ((2292.538 17264.27...       2
3  POLYGON ((2292.538 18563.3,...       3
4  POLYGON ((2292.538 19862.34...       4
5  POLYGON ((2292.538 21161.38...       5
6  POLYGON ((2292.538 22460.42...       6
7  POLYGON ((2292.538 23759.46...       7
8  POLYGON ((2292.538 25058.49...       8
9  POLYGON ((2292.538 26357.53...       9
10 POLYGON ((2292.538 27656.57...      10

This will give us a hexagon grid as seen below.

Show the code
qtm(hex_grid_sf)

To make the entire Singapore map into a hexagon grid, we use st_intersects() to find out the “overlap” between the entire hexagon grid and the Singapore map (as outlined by mpsz3414). We use lengths() to return the number of each element of the list then attach it as a column back to hex_grid_sf data frame.

Show the code
hex_grid_sf$SG <- lengths(st_intersects(hex_grid_sf, mpsz3414))

We then use this column to “cut out” the hexagon grid in Singapore map shape by filtering out values in the SG column that do not contain 0 because 0 means there is no overlap between mpsz and the hexagon grid.

Show the code
sgmap <- filter(hex_grid_sf, SG>0)

head(sgmap, 10) 
Simple feature collection with 10 features and 2 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 2292.538 ymin: 21810.9 xmax: 3417.538 ymax: 28522.6
Projected CRS: SVY21 / Singapore TM
                         hex_grid grid_id SG
1  POLYGON ((2667.538 21810.9,...      33  1
2  POLYGON ((2667.538 23109.94...      34  1
3  POLYGON ((2667.538 24408.98...      35  1
4  POLYGON ((2667.538 25708.01...      36  1
5  POLYGON ((2667.538 27007.05...      37  1
6  POLYGON ((3042.538 22460.42...      60  1
7  POLYGON ((3042.538 23759.46...      61  1
8  POLYGON ((3042.538 25058.49...      62  1
9  POLYGON ((3042.538 26357.53...      63  1
10 POLYGON ((3042.538 27656.57...      64  1

We plot out sgmap to check that the entire Singapore map is now broken into hexagon units, rather than planning subzones.

Show the code
qtm(sgmap)

We use st_intersects() and lengths() to find out how many businesses, Financial Services, MRT Exits, Busstops, HDB Commercial buildings, HDB Residential Buildings are in each hexagon.

Show the code
sgmap$`BIZ_COUNT` <- lengths(st_intersects(sgmap, business3414))
sgmap$`FINSERV_COUNT` <- lengths(st_intersects(sgmap, finserv3414))
sgmap$`MRTEXIT_COUNT` <- lengths(st_intersects(sgmap, mrtexits3414))
sgmap$`BUSSTOPS_COUNT` <- lengths(st_intersects(sgmap, busstop3414))
sgmap$`HDBCOMMERCIAL_COUNT` <- lengths(st_intersects(sgmap, hdb_commercial_sf))
sgmap$`HDBRESIDENTIAL_COUNT` <- lengths(st_intersects(sgmap, hdb_residental_sf))
sgmap$`SCHOOLS_COUNT` <- lengths(st_intersects(sgmap, schools_sf))

glimpse(sgmap)
Rows: 1,945
Columns: 10
$ hex_grid             <POLYGON [m]> POLYGON ((2667.538 21810.9,..., POLYGON (…
$ grid_id              <int> 33, 34, 35, 36, 37, 60, 61, 62, 63, 64, 87, 88, 8…
$ SG                   <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ FINSERV_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ BUSSTOPS_COUNT       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ HDBCOMMERCIAL_COUNT  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ HDBRESIDENTIAL_COUNT <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…

Notice that the sgmap has hexagon related information and the counts of the businesses, financial services, HDB commercial buildings, HDB residential buildings, schools, MRT exits and bus stops in each hexagon, but we are unable to map it back to the odbus_WDMP data because there are no common fields.

Hence, we will use st_intersection() to perform point (busstop3414) and polygon (sgmap) overlay. The output will be in point sf object.

Show the code
busstop_hex <- st_intersection(busstop3414, sgmap)
glimpse(busstop_hex)
Rows: 5,156
Columns: 13
$ BUS_STOP_N           <chr> "25059", "25751", "26379", "26299", "25761", "263…
$ BUS_ROOF_N           <chr> "UNK", "B02D", "NIL", "B13", "B03", "NIL", "B01C"…
$ LOC_DESC             <chr> "AFT TUAS STH BLVD", "BEF TUAS STH AVE 14", "YONG…
$ grid_id              <int> 118, 146, 174, 175, 200, 201, 201, 201, 201, 202,…
$ SG                   <int> 1, 1, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1…
$ BIZ_COUNT            <int> 0, 3, 49, 0, 2, 14, 14, 14, 14, 75, 75, 29, 29, 3…
$ FINSERV_COUNT        <int> 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0…
$ MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ BUSSTOPS_COUNT       <int> 1, 1, 1, 1, 1, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 4, 4…
$ HDBCOMMERCIAL_COUNT  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ HDBRESIDENTIAL_COUNT <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ geometry             <POINT [m]> POINT (3970.122 28063.28), POINT (4427.939 …

The output shows that we now know which bus stops are in which grid using the grid id.

We also intersect mpsz with sgmap to get the subzones and their corresponding grid id.

Show the code
mpsz_hex <- st_intersection(mpsz3414, sgmap)
glimpse(mpsz_hex)
Rows: 3,688
Columns: 16
$ SUBZONE_N            <chr> "TUAS VIEW EXTENSION", "TUAS VIEW EXTENSION", "TU…
$ SUBZONE_C            <chr> "TSSZ06", "TSSZ06", "TSSZ06", "TSSZ06", "TSSZ06",…
$ PLN_AREA_N           <chr> "TUAS", "TUAS", "TUAS", "TUAS", "TUAS", "TUAS", "…
$ PLN_AREA_C           <chr> "TS", "TS", "TS", "TS", "TS", "TS", "TS", "TS", "…
$ REGION_N             <chr> "WEST REGION", "WEST REGION", "WEST REGION", "WES…
$ REGION_C             <chr> "WR", "WR", "WR", "WR", "WR", "WR", "WR", "WR", "…
$ grid_id              <int> 33, 34, 35, 36, 37, 60, 61, 62, 63, 64, 87, 88, 8…
$ SG                   <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ FINSERV_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ BUSSTOPS_COUNT       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ HDBCOMMERCIAL_COUNT  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ HDBRESIDENTIAL_COUNT <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ geometry             <GEOMETRY [m]> POLYGON ((3040.877 22392.98..., POLYGON …

We then combine busstop_hex and mpsz_hex to get the busstops, their grid_id, the subzones they are in and the count of the various factors affecting commuter flows

Show the code
busstop_hex_mpsz <- st_intersection(busstop_hex, mpsz_hex) %>%
  select(BUS_STOP_N,LOC_DESC,
         grid_id,BIZ_COUNT,
         FINSERV_COUNT,MRTEXIT_COUNT,BUSSTOPS_COUNT, 
         HDBCOMMERCIAL_COUNT,HDBRESIDENTIAL_COUNT,
         SCHOOLS_COUNT,SUBZONE_N,SUBZONE_C)

glimpse(busstop_hex_mpsz)
Rows: 5,156
Columns: 13
$ BUS_STOP_N           <chr> "25059", "25751", "26379", "26299", "25761", "263…
$ LOC_DESC             <chr> "AFT TUAS STH BLVD", "BEF TUAS STH AVE 14", "YONG…
$ grid_id              <int> 118, 146, 174, 175, 200, 201, 201, 201, 201, 202,…
$ BIZ_COUNT            <int> 0, 3, 49, 0, 2, 14, 14, 14, 14, 75, 75, 29, 29, 3…
$ FINSERV_COUNT        <int> 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0…
$ MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ BUSSTOPS_COUNT       <int> 1, 1, 1, 1, 1, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 4, 4…
$ HDBCOMMERCIAL_COUNT  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ HDBRESIDENTIAL_COUNT <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ SUBZONE_N            <chr> "TUAS VIEW EXTENSION", "TUAS VIEW EXTENSION", "TU…
$ SUBZONE_C            <chr> "TSSZ06", "TSSZ06", "TSSZ05", "TSSZ05", "TSSZ06",…
$ geometry             <POINT [m]> POINT (3970.122 28063.28), POINT (4427.939 …
Note

Note that after we combined busstop_hex with mpsz_hex, the number of observations dropped from 5161 to 5156. This is because there are 5 busstops outside of Singapore.

2.4 Visualising the Attractiveness/ Propulsiveness Factors

We use the following code chunk to visualise the distribution of businesses over the hexagon grid of singapore map.

summary(sgmap$BIZ_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   0.000   3.368   1.000 126.000 
Show the code
tmap_mode("plot")

  tm_shape(sgmap) +
  tm_fill("BIZ_COUNT", title = "Number of Businesses") + 
  tm_borders(alpha = 0.5) +
  tm_layout(main.title = "Number of Businesses Per Grid",
            main.title.position = "center",
            main.title.size = 1,
            legend.height = 0.35, 
            legend.width = 0.35,
            legend.outside = FALSE,
            legend.position = c("right", "bottom"),
            frame = FALSE)  

datatable(sgmap %>% 
  select(grid_id,BIZ_COUNT) %>%
  arrange(desc(sgmap$BIZ_COUNT)))

From the above output, we observe that grid 2419 has the highest number of businesses concentrated, followed by grid 1673, 717 and 2009. Overall, the western part of Singapore has a larger concentration of businesses. This could be due to there having more factories and industrial estates in that area.

summary(sgmap$FINSERV_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   0.000   1.707   0.000 176.000 
tmap_mode("plot")
tm_shape(sgmap) +
  tm_fill("FINSERV_COUNT", title = "Number of Financial Services") + 
  tm_borders(alpha = 0.5) +
  tm_layout(main.title = "Number of Financial Services Per Grid",
            main.title.position = "center",
            main.title.size = 1,
            legend.height = 0.35, 
            legend.width = 0.35,
            legend.outside = FALSE,
            legend.position = c("right", "bottom"),
            frame = FALSE) 

datatable(sgmap %>% 
  select(grid_id,FINSERV_COUNT) %>%
  arrange(desc(sgmap$FINSERV_COUNT)))
summary(sgmap$MRTEXIT_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.2905  0.0000 19.0000 
tmap_mode("plot")
tm_shape(sgmap) +
  tm_fill("MRTEXIT_COUNT", title = "Number of MRT Exits") + 
  tm_borders(alpha = 0.5) +
  tm_layout(main.title = "Number of MRT EXIT Per Grid",
            main.title.position = "center",
            main.title.size = 1,
            legend.height = 0.35, 
            legend.width = 0.35,
            legend.outside = FALSE,
            legend.position = c("right", "bottom"),
            frame = FALSE) 

datatable(sgmap %>% 
  select(grid_id,MRTEXIT_COUNT) %>%
  arrange(desc(sgmap$MRTEXIT_COUNT)))
summary(sgmap$BUSSTOPS_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   0.000   2.651   5.000  20.000 
tmap_mode("plot")
tm_shape(sgmap) +
  tm_fill("BUSSTOPS_COUNT", title = "Number of Bus Stops") + 
  tm_borders(alpha = 0.5) +
  tm_layout(main.title = "Number of Bus Stops Per Grid",
            main.title.position = "center",
            main.title.size = 1,
            legend.height = 0.35, 
            legend.width = 0.35,
            legend.outside = FALSE,
            legend.position = c("right", "bottom"),
            frame = FALSE) 

datatable(sgmap %>% 
  select(grid_id,BUSSTOPS_COUNT) %>%
  arrange(desc(sgmap$BUSSTOPS_COUNT)))

3 Creating O-D Matrix

To visualise the commuter flows from orgin busstops to destination busstops, we need to create an Origin-Destination Matrix. First, we will convert the busstop_hex_mpsz (sf dataframe) to a tibble dataframe using st_drop_geometry().

Show the code
busstop_hex_mpsz_df <- busstop_hex_mpsz %>%
  st_drop_geometry()

glimpse(busstop_hex_mpsz_df)
Rows: 5,156
Columns: 12
$ BUS_STOP_N           <chr> "25059", "25751", "26379", "26299", "25761", "263…
$ LOC_DESC             <chr> "AFT TUAS STH BLVD", "BEF TUAS STH AVE 14", "YONG…
$ grid_id              <int> 118, 146, 174, 175, 200, 201, 201, 201, 201, 202,…
$ BIZ_COUNT            <int> 0, 3, 49, 0, 2, 14, 14, 14, 14, 75, 75, 29, 29, 3…
$ FINSERV_COUNT        <int> 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0…
$ MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ BUSSTOPS_COUNT       <int> 1, 1, 1, 1, 1, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 4, 4…
$ HDBCOMMERCIAL_COUNT  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ HDBRESIDENTIAL_COUNT <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ SUBZONE_N            <chr> "TUAS VIEW EXTENSION", "TUAS VIEW EXTENSION", "TU…
$ SUBZONE_C            <chr> "TSSZ06", "TSSZ06", "TSSZ05", "TSSZ05", "TSSZ06",…

With this dataframe, we can join it with the odbus_WDMP dataframe, which contains the passenger volume data.

Show the code
od_data <- left_join(odbus_WDMP, busstop_hex_mpsz_df,
                     by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
  rename(ORIGIN_BS = ORIGIN_PT_CODE,
         ORIGIN_SZ = SUBZONE_C,
         ORIGIN_SZN = SUBZONE_N,
         DESTIN_BS = DESTINATION_PT_CODE,
         ORIGIN_BIZ_COUNT = BIZ_COUNT,
         ORIGIN_FINSERV_COUNT = FINSERV_COUNT,
         ORIGIN_MRTEXIT_COUNT = MRTEXIT_COUNT,
         ORIGIN_BUSSTOP_COUNT = BUSSTOPS_COUNT,
         ORIGIN_HDBCOMMERCIAL_COUNT = HDBCOMMERCIAL_COUNT,
         ORIGIN_HDBRESIDENTIAL_COUNT = HDBRESIDENTIAL_COUNT,
         ORIGIN_SCHOOLS_COUNT = SCHOOLS_COUNT,
         ORIGIN_LOC_DESC = LOC_DESC,
         ORIGIN_GRID_ID = grid_id)

glimpse(od_data)
Rows: 242,944
Columns: 14
Groups: ORIGIN_BS [5,029]
$ ORIGIN_BS                   <chr> "01012", "01012", "01012", "01012", "01012…
$ DESTIN_BS                   <fct> 01112, 01113, 01121, 01211, 01311, 07371, …
$ TRIPS                       <dbl> 290, 118, 77, 118, 165, 14, 30, 16, 35, 26…
$ ORIGIN_LOC_DESC             <chr> "HOTEL GRAND PACIFIC", "HOTEL GRAND PACIFI…
$ ORIGIN_GRID_ID              <int> 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
$ ORIGIN_BIZ_COUNT            <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21…
$ ORIGIN_FINSERV_COUNT        <int> 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46…
$ ORIGIN_MRTEXIT_COUNT        <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, …
$ ORIGIN_BUSSTOP_COUNT        <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15…
$ ORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_HDBRESIDENTIAL_COUNT <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ORIGIN_SZN                  <chr> "VICTORIA", "VICTORIA", "VICTORIA", "VICTO…
$ ORIGIN_SZ                   <chr> "RCSZ10", "RCSZ10", "RCSZ10", "RCSZ10", "R…

From the above output, we use the following code chunk to convert ORIGIN_BS into a factor since ORIGIN_BS contains the origin bus stop numbers.

Show the code
od_data$ORIGIN_BS <- as.factor(od_data$ORIGIN_BS)
glimpse(od_data)
Rows: 242,944
Columns: 14
Groups: ORIGIN_BS [5,029]
$ ORIGIN_BS                   <fct> 01012, 01012, 01012, 01012, 01012, 01012, …
$ DESTIN_BS                   <fct> 01112, 01113, 01121, 01211, 01311, 07371, …
$ TRIPS                       <dbl> 290, 118, 77, 118, 165, 14, 30, 16, 35, 26…
$ ORIGIN_LOC_DESC             <chr> "HOTEL GRAND PACIFIC", "HOTEL GRAND PACIFI…
$ ORIGIN_GRID_ID              <int> 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
$ ORIGIN_BIZ_COUNT            <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21…
$ ORIGIN_FINSERV_COUNT        <int> 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46…
$ ORIGIN_MRTEXIT_COUNT        <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, …
$ ORIGIN_BUSSTOP_COUNT        <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15…
$ ORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_HDBRESIDENTIAL_COUNT <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ORIGIN_SZN                  <chr> "VICTORIA", "VICTORIA", "VICTORIA", "VICTO…
$ ORIGIN_SZ                   <chr> "RCSZ10", "RCSZ10", "RCSZ10", "RCSZ10", "R…

We now check for duplicates in the od_data frame.

Show the code
duplicate4 <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

datatable(duplicate4)

From the above output, we find that there are 700 duplicate entries. Hence we will use the following code chunk to remove the duplicates.

Show the code
od_data <- unique(od_data)

We will run the following code chunk to confirm that all duplicates have been removed.

Show the code
duplicate5 <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

duplicate5
# A tibble: 0 × 14
# ℹ 14 variables: ORIGIN_BS <fct>, DESTIN_BS <fct>, TRIPS <dbl>,
#   ORIGIN_LOC_DESC <chr>, ORIGIN_GRID_ID <int>, ORIGIN_BIZ_COUNT <int>,
#   ORIGIN_FINSERV_COUNT <int>, ORIGIN_MRTEXIT_COUNT <int>,
#   ORIGIN_BUSSTOP_COUNT <int>, ORIGIN_HDBCOMMERCIAL_COUNT <int>,
#   ORIGIN_HDBRESIDENTIAL_COUNT <int>, ORIGIN_SCHOOLS_COUNT <int>,
#   ORIGIN_SZN <chr>, ORIGIN_SZ <chr>

Now we will join the od_data dataframe with the busstop_hex_mpsz_df using the DESTIN_BS. By joining these two dataframes using the Destination Busstops, we can get the counts of the attractiveness/ propelsive factors at the destination.

Show the code
od_data <- left_join(od_data , busstop_hex_mpsz_df,
            by = c("DESTIN_BS" = "BUS_STOP_N")) %>%
  rename(DESTIN_SZ = SUBZONE_C,
         DESTIN_SZN = SUBZONE_N,
         DESTIN_BIZ_COUNT = BIZ_COUNT,
         DESTIN_FINSERV_COUNT = FINSERV_COUNT,
         DESTIN_MRTEXIT_COUNT = MRTEXIT_COUNT,
         DESTIN_BUSSTOP_COUNT = BUSSTOPS_COUNT,
         DESTIN_HDBCOMMERCIAL_COUNT = HDBCOMMERCIAL_COUNT,
         DESTIN_HDBRESIDENTIAL_COUNT = HDBRESIDENTIAL_COUNT,
         DESTIN_SCHOOLS_COUNT = SCHOOLS_COUNT,
         DESTIN_LOC_DESC = LOC_DESC,
         DESTIN_GRID_ID = grid_id)
Show the code
glimpse(od_data)
Rows: 243,506
Columns: 25
Groups: ORIGIN_BS [5,029]
$ ORIGIN_BS                   <fct> 01012, 01012, 01012, 01012, 01012, 01012, …
$ DESTIN_BS                   <chr> "01112", "01113", "01121", "01211", "01311…
$ TRIPS                       <dbl> 290, 118, 77, 118, 165, 14, 30, 16, 35, 26…
$ ORIGIN_LOC_DESC             <chr> "HOTEL GRAND PACIFIC", "HOTEL GRAND PACIFI…
$ ORIGIN_GRID_ID              <int> 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
$ ORIGIN_BIZ_COUNT            <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21…
$ ORIGIN_FINSERV_COUNT        <int> 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46…
$ ORIGIN_MRTEXIT_COUNT        <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, …
$ ORIGIN_BUSSTOP_COUNT        <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15…
$ ORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_HDBRESIDENTIAL_COUNT <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ORIGIN_SZN                  <chr> "VICTORIA", "VICTORIA", "VICTORIA", "VICTO…
$ ORIGIN_SZ                   <chr> "RCSZ10", "RCSZ10", "RCSZ10", "RCSZ10", "R…
$ DESTIN_LOC_DESC             <chr> "OPP BUGIS STN EXIT C", "BUGIS STN EXIT B"…
$ DESTIN_GRID_ID              <int> 2038, 2038, 2065, 2065, 2119, 2093, 2093, …
$ DESTIN_BIZ_COUNT            <int> 45, 45, 22, 22, 5, 31, 31, 29, 1, 1, 34, 1…
$ DESTIN_FINSERV_COUNT        <int> 53, 53, 25, 25, 40, 15, 15, 5, 6, 6, 7, 6,…
$ DESTIN_MRTEXIT_COUNT        <int> 4, 4, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 0, 0, …
$ DESTIN_BUSSTOP_COUNT        <int> 20, 20, 9, 9, 8, 10, 10, 6, 7, 7, 10, 7, 4…
$ DESTIN_HDBCOMMERCIAL_COUNT  <int> 5, 5, 21, 21, 11, 3, 3, 5, 14, 14, 0, 14, …
$ DESTIN_HDBRESIDENTIAL_COUNT <int> 10, 10, 23, 23, 15, 3, 3, 11, 35, 35, 0, 3…
$ DESTIN_SCHOOLS_COUNT        <int> 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, …
$ DESTIN_SZN                  <chr> "VICTORIA", "BUGIS", "ROCHOR CANAL", "CRAW…
$ DESTIN_SZ                   <chr> "RCSZ10", "DTSZ01", "RCSZ04", "KLSZ09", "K…

Let us convert DESTIN_BS, ORIGIN_GRID_ID and DESTIN_GRID_ID to factors.

Show the code
od_data$DESTIN_BS <- as.factor(od_data$DESTIN_BS)
od_data$ORIGIN_GRID_ID <- as.factor(od_data$ORIGIN_GRID_ID)
od_data$DESTIN_GRID_ID <- as.factor(od_data$DESTIN_GRID_ID)

We will check for duplicates to ensure that each origin only has 1 line that goes to a particular destination.

Show the code
duplicate6 <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

datatable(duplicate6)

We use the following code chunk to remove the duplicates.

Show the code
od_data <- unique(od_data)

We run the following code chunk to ensure that all duplicates have been removed.

Show the code
duplicate7 <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

duplicate7
# A tibble: 0 × 25
# ℹ 25 variables: ORIGIN_BS <fct>, DESTIN_BS <fct>, TRIPS <dbl>,
#   ORIGIN_LOC_DESC <chr>, ORIGIN_GRID_ID <fct>, ORIGIN_BIZ_COUNT <int>,
#   ORIGIN_FINSERV_COUNT <int>, ORIGIN_MRTEXIT_COUNT <int>,
#   ORIGIN_BUSSTOP_COUNT <int>, ORIGIN_HDBCOMMERCIAL_COUNT <int>,
#   ORIGIN_HDBRESIDENTIAL_COUNT <int>, ORIGIN_SCHOOLS_COUNT <int>,
#   ORIGIN_SZN <chr>, ORIGIN_SZ <chr>, DESTIN_LOC_DESC <chr>,
#   DESTIN_GRID_ID <fct>, DESTIN_BIZ_COUNT <int>, DESTIN_FINSERV_COUNT <int>, …

Let us take a look at the od_data again before we move on.

Show the code
glimpse(od_data)
Rows: 243,101
Columns: 25
Groups: ORIGIN_BS [5,029]
$ ORIGIN_BS                   <fct> 01012, 01012, 01012, 01012, 01012, 01012, …
$ DESTIN_BS                   <fct> 01112, 01113, 01121, 01211, 01311, 07371, …
$ TRIPS                       <dbl> 290, 118, 77, 118, 165, 14, 30, 16, 35, 26…
$ ORIGIN_LOC_DESC             <chr> "HOTEL GRAND PACIFIC", "HOTEL GRAND PACIFI…
$ ORIGIN_GRID_ID              <fct> 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
$ ORIGIN_BIZ_COUNT            <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21…
$ ORIGIN_FINSERV_COUNT        <int> 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46…
$ ORIGIN_MRTEXIT_COUNT        <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, …
$ ORIGIN_BUSSTOP_COUNT        <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15…
$ ORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_HDBRESIDENTIAL_COUNT <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ORIGIN_SZN                  <chr> "VICTORIA", "VICTORIA", "VICTORIA", "VICTO…
$ ORIGIN_SZ                   <chr> "RCSZ10", "RCSZ10", "RCSZ10", "RCSZ10", "R…
$ DESTIN_LOC_DESC             <chr> "OPP BUGIS STN EXIT C", "BUGIS STN EXIT B"…
$ DESTIN_GRID_ID              <fct> 2038, 2038, 2065, 2065, 2119, 2093, 2093, …
$ DESTIN_BIZ_COUNT            <int> 45, 45, 22, 22, 5, 31, 31, 29, 1, 1, 34, 1…
$ DESTIN_FINSERV_COUNT        <int> 53, 53, 25, 25, 40, 15, 15, 5, 6, 6, 7, 6,…
$ DESTIN_MRTEXIT_COUNT        <int> 4, 4, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 0, 0, …
$ DESTIN_BUSSTOP_COUNT        <int> 20, 20, 9, 9, 8, 10, 10, 6, 7, 7, 10, 7, 4…
$ DESTIN_HDBCOMMERCIAL_COUNT  <int> 5, 5, 21, 21, 11, 3, 3, 5, 14, 14, 0, 14, …
$ DESTIN_HDBRESIDENTIAL_COUNT <int> 10, 10, 23, 23, 15, 3, 3, 11, 35, 35, 0, 3…
$ DESTIN_SCHOOLS_COUNT        <int> 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, …
$ DESTIN_SZN                  <chr> "VICTORIA", "BUGIS", "ROCHOR CANAL", "CRAW…
$ DESTIN_SZ                   <chr> "RCSZ10", "DTSZ01", "RCSZ04", "KLSZ09", "K…

However, we note that the hdb_commerical and hdb residential dataframes have dwelling numbers for each building. Currently we only have the counts of HDB commercial and residential buildings in od_data. The counts of these buildings might not be as useful or representative because a grid can have many low dwelling number HDB residential building. Hence, we will add the total dwelling numbers from hdb commercial and hdb residential into the sgmap dataframe.

First let us add grid_id to the hdb_commercial_sf so that we can later join it to the sgmap dataframe so that they can be assigned with a grid_id. We will also select the relevant columns that we want using the following code chunk.

Show the code
hdb_commercial_hex <- st_intersection(hdb_commercial_sf, sgmap) %>%
  st_drop_geometry() %>%
  select(postal, SUBZONE_N, total_dwelling_units, grid_id)

glimpse(hdb_commercial_hex) 
Rows: 2,508
Columns: 4
$ postal               <chr> "640907", "640909", "640920", "640932", "640943",…
$ SUBZONE_N            <chr> "YUNNAN", "YUNNAN", "YUNNAN", "YUNNAN", "YUNNAN",…
$ total_dwelling_units <dbl> 77, 110, 120, 144, 90, 88, 72, 0, 0, 66, 0, 0, 0,…
$ grid_id              <int> 664, 664, 718, 718, 718, 718, 718, 718, 718, 718,…

Notice that a few postal codes can be in 1 grid, so we will use group_by() to sum up the total dwelling units in each hexagon unit.

Show the code
hdb_commercial_hex1 <- hdb_commercial_hex %>%
  group_by(grid_id)%>%
  summarise(total_comm_units_grid = sum(total_dwelling_units))

glimpse(hdb_commercial_hex1) 
Rows: 354
Columns: 2
$ grid_id               <int> 664, 718, 745, 746, 772, 799, 800, 826, 827, 854…
$ total_comm_units_grid <dbl> 187, 670, 96, 2032, 1278, 0, 1637, 428, 0, 556, …

We will convert the grid_id into a factor so that it is the same data type as the grid_id in od_data before joining them together.

Show the code
hdb_commercial_hex1$grid_id <- as.factor(hdb_commercial_hex1$grid_id)

We use the following code chunk to join od_data and hdb_commercial_hex1 together at the ORIGIN_GRID_ID. This will let us know the number of HDB Residential and Commercial dwellings at the ORIGIN_GRID_ID.

Show the code
od_data <- left_join(od_data, hdb_commercial_hex1,
                     by=c("ORIGIN_GRID_ID"= "grid_id"))%>%
  rename(ORIGIN_HDBCOMM_UNITS = total_comm_units_grid)

glimpse(od_data)
Rows: 243,101
Columns: 26
Groups: ORIGIN_BS [5,029]
$ ORIGIN_BS                   <fct> 01012, 01012, 01012, 01012, 01012, 01012, …
$ DESTIN_BS                   <fct> 01112, 01113, 01121, 01211, 01311, 07371, …
$ TRIPS                       <dbl> 290, 118, 77, 118, 165, 14, 30, 16, 35, 26…
$ ORIGIN_LOC_DESC             <chr> "HOTEL GRAND PACIFIC", "HOTEL GRAND PACIFI…
$ ORIGIN_GRID_ID              <fct> 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
$ ORIGIN_BIZ_COUNT            <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21…
$ ORIGIN_FINSERV_COUNT        <int> 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46…
$ ORIGIN_MRTEXIT_COUNT        <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, …
$ ORIGIN_BUSSTOP_COUNT        <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15…
$ ORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_HDBRESIDENTIAL_COUNT <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ORIGIN_SZN                  <chr> "VICTORIA", "VICTORIA", "VICTORIA", "VICTO…
$ ORIGIN_SZ                   <chr> "RCSZ10", "RCSZ10", "RCSZ10", "RCSZ10", "R…
$ DESTIN_LOC_DESC             <chr> "OPP BUGIS STN EXIT C", "BUGIS STN EXIT B"…
$ DESTIN_GRID_ID              <fct> 2038, 2038, 2065, 2065, 2119, 2093, 2093, …
$ DESTIN_BIZ_COUNT            <int> 45, 45, 22, 22, 5, 31, 31, 29, 1, 1, 34, 1…
$ DESTIN_FINSERV_COUNT        <int> 53, 53, 25, 25, 40, 15, 15, 5, 6, 6, 7, 6,…
$ DESTIN_MRTEXIT_COUNT        <int> 4, 4, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 0, 0, …
$ DESTIN_BUSSTOP_COUNT        <int> 20, 20, 9, 9, 8, 10, 10, 6, 7, 7, 10, 7, 4…
$ DESTIN_HDBCOMMERCIAL_COUNT  <int> 5, 5, 21, 21, 11, 3, 3, 5, 14, 14, 0, 14, …
$ DESTIN_HDBRESIDENTIAL_COUNT <int> 10, 10, 23, 23, 15, 3, 3, 11, 35, 35, 0, 3…
$ DESTIN_SCHOOLS_COUNT        <int> 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, …
$ DESTIN_SZN                  <chr> "VICTORIA", "BUGIS", "ROCHOR CANAL", "CRAW…
$ DESTIN_SZ                   <chr> "RCSZ10", "DTSZ01", "RCSZ04", "KLSZ09", "K…
$ ORIGIN_HDBCOMM_UNITS        <dbl> 280, 280, 280, 280, 280, 280, 280, 280, 28…

We use the following code chunk to join od_data and hdb_commercial_hex1 together at the DESTIN_GRID_ID. This will let us know the number of HDB Residential and Commercial dwellings at the DESTIN_GRID_ID.

Show the code
od_data <- left_join(od_data, hdb_commercial_hex1,
                     by=c("DESTIN_GRID_ID"= "grid_id"))%>%
  rename(DESTIN_HDBCOMM_UNITS = total_comm_units_grid)

glimpse(od_data)
Rows: 243,101
Columns: 27
Groups: ORIGIN_BS [5,029]
$ ORIGIN_BS                   <fct> 01012, 01012, 01012, 01012, 01012, 01012, …
$ DESTIN_BS                   <fct> 01112, 01113, 01121, 01211, 01311, 07371, …
$ TRIPS                       <dbl> 290, 118, 77, 118, 165, 14, 30, 16, 35, 26…
$ ORIGIN_LOC_DESC             <chr> "HOTEL GRAND PACIFIC", "HOTEL GRAND PACIFI…
$ ORIGIN_GRID_ID              <fct> 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
$ ORIGIN_BIZ_COUNT            <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21…
$ ORIGIN_FINSERV_COUNT        <int> 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46…
$ ORIGIN_MRTEXIT_COUNT        <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, …
$ ORIGIN_BUSSTOP_COUNT        <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15…
$ ORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_HDBRESIDENTIAL_COUNT <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ORIGIN_SZN                  <chr> "VICTORIA", "VICTORIA", "VICTORIA", "VICTO…
$ ORIGIN_SZ                   <chr> "RCSZ10", "RCSZ10", "RCSZ10", "RCSZ10", "R…
$ DESTIN_LOC_DESC             <chr> "OPP BUGIS STN EXIT C", "BUGIS STN EXIT B"…
$ DESTIN_GRID_ID              <fct> 2038, 2038, 2065, 2065, 2119, 2093, 2093, …
$ DESTIN_BIZ_COUNT            <int> 45, 45, 22, 22, 5, 31, 31, 29, 1, 1, 34, 1…
$ DESTIN_FINSERV_COUNT        <int> 53, 53, 25, 25, 40, 15, 15, 5, 6, 6, 7, 6,…
$ DESTIN_MRTEXIT_COUNT        <int> 4, 4, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 0, 0, …
$ DESTIN_BUSSTOP_COUNT        <int> 20, 20, 9, 9, 8, 10, 10, 6, 7, 7, 10, 7, 4…
$ DESTIN_HDBCOMMERCIAL_COUNT  <int> 5, 5, 21, 21, 11, 3, 3, 5, 14, 14, 0, 14, …
$ DESTIN_HDBRESIDENTIAL_COUNT <int> 10, 10, 23, 23, 15, 3, 3, 11, 35, 35, 0, 3…
$ DESTIN_SCHOOLS_COUNT        <int> 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, …
$ DESTIN_SZN                  <chr> "VICTORIA", "BUGIS", "ROCHOR CANAL", "CRAW…
$ DESTIN_SZ                   <chr> "RCSZ10", "DTSZ01", "RCSZ04", "KLSZ09", "K…
$ ORIGIN_HDBCOMM_UNITS        <dbl> 280, 280, 280, 280, 280, 280, 280, 280, 28…
$ DESTIN_HDBCOMM_UNITS        <dbl> 307, 307, 2246, 2246, 929, 0, 0, 374, 2133…

We will do the same for the HDB residential data frame.

Show the code
hdb_residential_hex <- st_intersection(hdb_residental_sf, sgmap) %>%
  st_drop_geometry() %>%
  select(postal, SUBZONE_N, total_dwelling_units, grid_id)

glimpse(hdb_residential_hex)
Rows: 10,181
Columns: 4
$ postal               <chr> "640903", "640904", "640905", "640906", "640907",…
$ SUBZONE_N            <chr> "YUNNAN", "YUNNAN", "YUNNAN", "YUNNAN", "YUNNAN",…
$ total_dwelling_units <dbl> 84, 110, 28, 90, 77, 110, 110, 90, 99, 96, 77, 20…
$ grid_id              <int> 664, 664, 664, 664, 664, 664, 664, 664, 692, 718,…

Notice that a few postal codes can be in 1 grid, so we will use group_by() to sum up the total dwelling units in each hexagon unit.

Show the code
hdb_residential_hex1 <- hdb_residential_hex %>%
  group_by(grid_id)%>%
  summarise(total_res_units_grid = sum(total_dwelling_units))

glimpse(hdb_residential_hex1)
Rows: 397
Columns: 2
$ grid_id              <int> 664, 692, 718, 745, 746, 772, 773, 799, 800, 826,…
$ total_res_units_grid <dbl> 699, 99, 4083, 1524, 4079, 6643, 567, 3641, 4851,…
Show the code
hdb_residential_hex1$grid_id <- as.factor(hdb_residential_hex1$grid_id)

od_data <- left_join(od_data, hdb_residential_hex1,
                     by=c("ORIGIN_GRID_ID"= "grid_id"))%>%
  rename(ORIGIN_HDBRES_UNITS = total_res_units_grid)

glimpse(od_data)
Rows: 243,101
Columns: 28
Groups: ORIGIN_BS [5,029]
$ ORIGIN_BS                   <fct> 01012, 01012, 01012, 01012, 01012, 01012, …
$ DESTIN_BS                   <fct> 01112, 01113, 01121, 01211, 01311, 07371, …
$ TRIPS                       <dbl> 290, 118, 77, 118, 165, 14, 30, 16, 35, 26…
$ ORIGIN_LOC_DESC             <chr> "HOTEL GRAND PACIFIC", "HOTEL GRAND PACIFI…
$ ORIGIN_GRID_ID              <fct> 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
$ ORIGIN_BIZ_COUNT            <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21…
$ ORIGIN_FINSERV_COUNT        <int> 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46…
$ ORIGIN_MRTEXIT_COUNT        <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, …
$ ORIGIN_BUSSTOP_COUNT        <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15…
$ ORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_HDBRESIDENTIAL_COUNT <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ORIGIN_SZN                  <chr> "VICTORIA", "VICTORIA", "VICTORIA", "VICTO…
$ ORIGIN_SZ                   <chr> "RCSZ10", "RCSZ10", "RCSZ10", "RCSZ10", "R…
$ DESTIN_LOC_DESC             <chr> "OPP BUGIS STN EXIT C", "BUGIS STN EXIT B"…
$ DESTIN_GRID_ID              <fct> 2038, 2038, 2065, 2065, 2119, 2093, 2093, …
$ DESTIN_BIZ_COUNT            <int> 45, 45, 22, 22, 5, 31, 31, 29, 1, 1, 34, 1…
$ DESTIN_FINSERV_COUNT        <int> 53, 53, 25, 25, 40, 15, 15, 5, 6, 6, 7, 6,…
$ DESTIN_MRTEXIT_COUNT        <int> 4, 4, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 0, 0, …
$ DESTIN_BUSSTOP_COUNT        <int> 20, 20, 9, 9, 8, 10, 10, 6, 7, 7, 10, 7, 4…
$ DESTIN_HDBCOMMERCIAL_COUNT  <int> 5, 5, 21, 21, 11, 3, 3, 5, 14, 14, 0, 14, …
$ DESTIN_HDBRESIDENTIAL_COUNT <int> 10, 10, 23, 23, 15, 3, 3, 11, 35, 35, 0, 3…
$ DESTIN_SCHOOLS_COUNT        <int> 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, …
$ DESTIN_SZN                  <chr> "VICTORIA", "BUGIS", "ROCHOR CANAL", "CRAW…
$ DESTIN_SZ                   <chr> "RCSZ10", "DTSZ01", "RCSZ04", "KLSZ09", "K…
$ ORIGIN_HDBCOMM_UNITS        <dbl> 280, 280, 280, 280, 280, 280, 280, 280, 28…
$ DESTIN_HDBCOMM_UNITS        <dbl> 307, 307, 2246, 2246, 929, 0, 0, 374, 2133…
$ ORIGIN_HDBRES_UNITS         <dbl> 280, 280, 280, 280, 280, 280, 280, 280, 28…
Show the code
od_data <- left_join(od_data, hdb_residential_hex1,
                     by=c("DESTIN_GRID_ID"= "grid_id"))%>%
  rename(DESTIN_HDBRES_UNITS = total_res_units_grid)

glimpse(od_data)
Rows: 243,101
Columns: 29
Groups: ORIGIN_BS [5,029]
$ ORIGIN_BS                   <fct> 01012, 01012, 01012, 01012, 01012, 01012, …
$ DESTIN_BS                   <fct> 01112, 01113, 01121, 01211, 01311, 07371, …
$ TRIPS                       <dbl> 290, 118, 77, 118, 165, 14, 30, 16, 35, 26…
$ ORIGIN_LOC_DESC             <chr> "HOTEL GRAND PACIFIC", "HOTEL GRAND PACIFI…
$ ORIGIN_GRID_ID              <fct> 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
$ ORIGIN_BIZ_COUNT            <int> 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21…
$ ORIGIN_FINSERV_COUNT        <int> 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46…
$ ORIGIN_MRTEXIT_COUNT        <int> 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, …
$ ORIGIN_BUSSTOP_COUNT        <int> 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15…
$ ORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_HDBRESIDENTIAL_COUNT <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
$ ORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ ORIGIN_SZN                  <chr> "VICTORIA", "VICTORIA", "VICTORIA", "VICTO…
$ ORIGIN_SZ                   <chr> "RCSZ10", "RCSZ10", "RCSZ10", "RCSZ10", "R…
$ DESTIN_LOC_DESC             <chr> "OPP BUGIS STN EXIT C", "BUGIS STN EXIT B"…
$ DESTIN_GRID_ID              <fct> 2038, 2038, 2065, 2065, 2119, 2093, 2093, …
$ DESTIN_BIZ_COUNT            <int> 45, 45, 22, 22, 5, 31, 31, 29, 1, 1, 34, 1…
$ DESTIN_FINSERV_COUNT        <int> 53, 53, 25, 25, 40, 15, 15, 5, 6, 6, 7, 6,…
$ DESTIN_MRTEXIT_COUNT        <int> 4, 4, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 0, 0, …
$ DESTIN_BUSSTOP_COUNT        <int> 20, 20, 9, 9, 8, 10, 10, 6, 7, 7, 10, 7, 4…
$ DESTIN_HDBCOMMERCIAL_COUNT  <int> 5, 5, 21, 21, 11, 3, 3, 5, 14, 14, 0, 14, …
$ DESTIN_HDBRESIDENTIAL_COUNT <int> 10, 10, 23, 23, 15, 3, 3, 11, 35, 35, 0, 3…
$ DESTIN_SCHOOLS_COUNT        <int> 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, …
$ DESTIN_SZN                  <chr> "VICTORIA", "BUGIS", "ROCHOR CANAL", "CRAW…
$ DESTIN_SZ                   <chr> "RCSZ10", "DTSZ01", "RCSZ04", "KLSZ09", "K…
$ ORIGIN_HDBCOMM_UNITS        <dbl> 280, 280, 280, 280, 280, 280, 280, 280, 28…
$ DESTIN_HDBCOMM_UNITS        <dbl> 307, 307, 2246, 2246, 929, 0, 0, 374, 2133…
$ ORIGIN_HDBRES_UNITS         <dbl> 280, 280, 280, 280, 280, 280, 280, 280, 28…
$ DESTIN_HDBRES_UNITS         <dbl> 1293, 1293, 3101, 3101, 2927, 402, 402, 19…

Checking if the dataframe has any duplicate data

Show the code
duplicate8 <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()

duplicate8
# A tibble: 0 × 29
# ℹ 29 variables: ORIGIN_BS <fct>, DESTIN_BS <fct>, TRIPS <dbl>,
#   ORIGIN_LOC_DESC <chr>, ORIGIN_GRID_ID <fct>, ORIGIN_BIZ_COUNT <int>,
#   ORIGIN_FINSERV_COUNT <int>, ORIGIN_MRTEXIT_COUNT <int>,
#   ORIGIN_BUSSTOP_COUNT <int>, ORIGIN_HDBCOMMERCIAL_COUNT <int>,
#   ORIGIN_HDBRESIDENTIAL_COUNT <int>, ORIGIN_SCHOOLS_COUNT <int>,
#   ORIGIN_SZN <chr>, ORIGIN_SZ <chr>, DESTIN_LOC_DESC <chr>,
#   DESTIN_GRID_ID <fct>, DESTIN_BIZ_COUNT <int>, DESTIN_FINSERV_COUNT <int>, …

Currently the trips are calculated from the origin busstops, but we want to analyse the commuter flows at hexagon level so we will group by the origin_grid_id and destin_grid_id, sum the trips generated from the bus stops in each hexagon grid, and take the mean of the variables counts because we have counted them at the hexagon level (so we do not want to sum them up)

Show the code
od_data2 <- od_data %>%
  drop_na() %>%
  group_by(ORIGIN_GRID_ID, DESTIN_GRID_ID) %>%
  summarise(MORNING_PEAK = sum(TRIPS),
            TORIGIN_BIZ_COUNT = ORIGIN_BIZ_COUNT,
            TORIGIN_FINSERV_COUNT = ORIGIN_FINSERV_COUNT,
            TORIGIN_MRTEXIT_COUNT = ORIGIN_MRTEXIT_COUNT,
            TORIGIN_BUSSTOP_COUNT = ORIGIN_BUSSTOP_COUNT,
            TORIGIN_HDBCOMMERCIAL_COUNT = ORIGIN_HDBCOMMERCIAL_COUNT,
            TORIGIN_HDBRESIDENTIAL_COUNT = ORIGIN_HDBRESIDENTIAL_COUNT,
            TORIGIN_SCHOOLS_COUNT = ORIGIN_SCHOOLS_COUNT,
            TORIGIN_HDBCOMM_UNITS = ORIGIN_HDBCOMM_UNITS, 
            TORIGIN_HDBRES_UNITS = ORIGIN_HDBRES_UNITS, 
            TDESTIN_BIZ_COUNT = DESTIN_BIZ_COUNT,
            TDESTIN_FINSERV_COUNT = DESTIN_FINSERV_COUNT,
            TDESTIN_MRTEXIT_COUNT = DESTIN_MRTEXIT_COUNT,
            TDESTIN_BUSSTOP_COUNT = DESTIN_BUSSTOP_COUNT,
            TDESTIN_HDBCOMMERCIAL_COUNT = DESTIN_HDBCOMMERCIAL_COUNT,
            TDESTIN_HDBRESIDENTIAL_COUNT = DESTIN_HDBRESIDENTIAL_COUNT,
            TDESTIN_SCHOOLS_COUNT = DESTIN_SCHOOLS_COUNT,
            TDESTIN_HDBCOMM_UNITS = DESTIN_HDBCOMM_UNITS,
            TDESTIN_HDBRES_UNITS = DESTIN_HDBRES_UNITS)
Show the code
glimpse(od_data2)
Rows: 106,095
Columns: 21
Groups: ORIGIN_GRID_ID, DESTIN_GRID_ID [22,950]
$ ORIGIN_GRID_ID               <fct> 664, 664, 664, 664, 664, 664, 664, 664, 6…
$ DESTIN_GRID_ID               <fct> 664, 746, 746, 772, 772, 772, 772, 772, 7…
$ MORNING_PEAK                 <dbl> 9, 13, 13, 241, 241, 241, 241, 241, 241, …
$ TORIGIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_FINSERV_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7,…
$ TORIGIN_MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_BUSSTOP_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13…
$ TORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13…
$ TORIGIN_HDBRESIDENTIAL_COUNT <int> 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 45…
$ TORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,…
$ TORIGIN_HDBCOMM_UNITS        <dbl> 187, 187, 187, 187, 187, 187, 187, 187, 1…
$ TORIGIN_HDBRES_UNITS         <dbl> 699, 699, 699, 699, 699, 699, 699, 699, 6…
$ TDESTIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0,…
$ TDESTIN_FINSERV_COUNT        <int> 2, 0, 0, 7, 7, 7, 7, 7, 7, 0, 3, 3, 3, 7,…
$ TDESTIN_MRTEXIT_COUNT        <int> 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 5, 5, 5, 0,…
$ TDESTIN_BUSSTOP_COUNT        <int> 2, 9, 9, 20, 20, 20, 20, 20, 20, 9, 11, 1…
$ TDESTIN_HDBCOMMERCIAL_COUNT  <int> 2, 21, 21, 16, 16, 16, 16, 16, 16, 2, 4, …
$ TDESTIN_HDBRESIDENTIAL_COUNT <int> 8, 51, 51, 63, 63, 63, 63, 63, 63, 35, 56…
$ TDESTIN_SCHOOLS_COUNT        <int> 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3,…
$ TDESTIN_HDBCOMM_UNITS        <dbl> 187, 2032, 2032, 1278, 1278, 1278, 1278, …
$ TDESTIN_HDBRES_UNITS         <dbl> 699, 4079, 4079, 6643, 6643, 6643, 6643, …
Show the code
write_rds(od_data2, "data/rds/od_data.rds")

4 Geovisualisation of OD flows

As we are not plotting intra-zonal flows, the following code chunk removes the intra-zonal flows.

Show the code
od_data_interzone <- od_data2[od_data2$ORIGIN_GRID_ID != od_data2$DESTIN_GRID_ID,]

head(od_data_interzone)
# A tibble: 6 × 21
# Groups:   ORIGIN_GRID_ID, DESTIN_GRID_ID [2]
  ORIGIN_GRID_ID DESTIN_GRID_ID MORNING_PEAK TORIGIN_BIZ_COUNT
  <fct>          <fct>                 <dbl>             <int>
1 664            746                      13                 0
2 664            746                      13                 0
3 664            772                     241                 0
4 664            772                     241                 0
5 664            772                     241                 0
6 664            772                     241                 0
# ℹ 17 more variables: TORIGIN_FINSERV_COUNT <int>,
#   TORIGIN_MRTEXIT_COUNT <int>, TORIGIN_BUSSTOP_COUNT <int>,
#   TORIGIN_HDBCOMMERCIAL_COUNT <int>, TORIGIN_HDBRESIDENTIAL_COUNT <int>,
#   TORIGIN_SCHOOLS_COUNT <int>, TORIGIN_HDBCOMM_UNITS <dbl>,
#   TORIGIN_HDBRES_UNITS <dbl>, TDESTIN_BIZ_COUNT <int>,
#   TDESTIN_FINSERV_COUNT <int>, TDESTIN_MRTEXIT_COUNT <int>,
#   TDESTIN_BUSSTOP_COUNT <int>, TDESTIN_HDBCOMMERCIAL_COUNT <int>, …

4.1 Creating desire lines

Show the code
flowline <- od2line(flow=od_data_interzone, 
                    zones = sgmap,
                    zone_code = "grid_id")

glimpse(flowline)
Rows: 101,715
Columns: 22
$ ORIGIN_GRID_ID               <fct> 664, 664, 664, 664, 664, 664, 664, 664, 6…
$ DESTIN_GRID_ID               <fct> 746, 746, 772, 772, 772, 772, 772, 772, 7…
$ MORNING_PEAK                 <dbl> 13, 13, 241, 241, 241, 241, 241, 241, 1, …
$ TORIGIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_FINSERV_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7,…
$ TORIGIN_MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_BUSSTOP_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13, 1…
$ TORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13, 1…
$ TORIGIN_HDBRESIDENTIAL_COUNT <int> 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 45, 4…
$ TORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3,…
$ TORIGIN_HDBCOMM_UNITS        <dbl> 187, 187, 187, 187, 187, 187, 187, 187, 1…
$ TORIGIN_HDBRES_UNITS         <dbl> 699, 699, 699, 699, 699, 699, 699, 699, 6…
$ TDESTIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 41, 4…
$ TDESTIN_FINSERV_COUNT        <int> 0, 0, 7, 7, 7, 7, 7, 7, 0, 3, 3, 3, 1, 1,…
$ TDESTIN_MRTEXIT_COUNT        <int> 0, 0, 2, 2, 2, 2, 2, 2, 0, 5, 5, 5, 0, 0,…
$ TDESTIN_BUSSTOP_COUNT        <int> 9, 9, 20, 20, 20, 20, 20, 20, 9, 11, 11, …
$ TDESTIN_HDBCOMMERCIAL_COUNT  <int> 21, 21, 16, 16, 16, 16, 16, 16, 2, 4, 4, …
$ TDESTIN_HDBRESIDENTIAL_COUNT <int> 51, 51, 63, 63, 63, 63, 63, 63, 35, 56, 5…
$ TDESTIN_SCHOOLS_COUNT        <int> 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 0, 0,…
$ TDESTIN_HDBCOMM_UNITS        <dbl> 2032, 2032, 1278, 1278, 1278, 1278, 1278,…
$ TDESTIN_HDBRES_UNITS         <dbl> 4079, 4079, 6643, 6643, 6643, 6643, 6643,…
$ geometry                     <LINESTRING [m]> LINESTRING (11292.54 35883....…

Let us take a look at the summary statistics of the morning peak trips using summary().

Show the code
summary(flowline$MORNING_PEAK)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      1      63     300    1826    1297   87864 

From the above output, we see that the range of morning peak trips is wide. The number of trips can be as low as one and as high as 87,864. We can also deduce that the trips volume is extreme by looking at the difference between mean and median values. The mean is 1826 while the median is 300, meaning that there are few extreme high values (hence causing a relatively high mean) and many extreme low values (causing a relatively low median).

Let us break he morning peak trips into the various quantiles from 10th to the 100th quantile.

Show the code
quantile(flowline$MORNING_PEAK, probs = seq(.1, 1, by =.05))
  10%   15%   20%   25%   30%   35%   40%   45%   50%   55%   60%   65%   70% 
   15    27    42    63    92   127   171   224   300   394   533   711   941 
  75%   80%   85%   90%   95%  100% 
 1297  1858  2707  4192  8295 87864 

Let us plot out the flowlines from the 95th percentile onwards.

tm_shape(sgmap) +
  tm_polygons("BUSSTOPS_COUNT") + 
  flowline %>%
  filter(MORNING_PEAK >= 8295) %>%
  tm_shape() + 
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)+
    tm_layout(main.title = "Flow for Passenger Volume at 95th Percentile and Above",
            main.title.size = 0.9,
            main.title.position = "center")

flowline_95 <- flowline %>%
  filter(flowline$MORNING_PEAK >= 8295)

datatable(flowline_95)

Let us visualise the distribution of the trips from the 95th percentile and above using a histogram.

Show the code
ggplot(flowline_95, aes(x=MORNING_PEAK))+
  geom_histogram(binwidth = 2000, fill="#69b3a2", color="#e9ecef", alpha=0.9)+
  xlim(8000, 87900)

From the above output, we see that there are many

We will use summary() to look at the summary statistics for the

Show the code
summary(flowline_95$MORNING_PEAK)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   8295   10573   13881   19180   22622   87864 
Show the code
tmap_mode("plot")
tm_shape(sgmap) +
  tm_polygons("BUSSTOPS_COUNT") + 
  flowline %>%
  filter(MORNING_PEAK >= 8295, MORNING_PEAK<11000) %>%
  tm_shape() + 
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)+
    tm_layout(main.title = "Flow for Passenger Volume between 8295 and 11000",
            main.title.size = 0.9,
            main.title.position = "center")

Show the code
tm_shape(sgmap) +
  tm_polygons("BUSSTOPS_COUNT") + 
  flowline %>%
  filter(MORNING_PEAK>= 11000, MORNING_PEAK<14000) %>%
  tm_shape() + 
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)+
    tm_layout(main.title = "Flow for Passenger Volume between 11000 and 14000",
            main.title.size = 0.9,
            main.title.position = "center")

Show the code
tm_shape(sgmap) +
  tm_polygons("BUSSTOPS_COUNT") + 
  flowline %>%
  filter(MORNING_PEAK >= 14000, MORNING_PEAK<23000) %>%
  tm_shape() + 
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)+
    tm_layout(main.title = "Flow for Passenger Volume between 14000 and 23000",
            main.title.size = 0.9,
            main.title.position = "center")

Show the code
tm_shape(sgmap) +
  tm_polygons("BUSSTOPS_COUNT") + 
  flowline %>%
  filter(MORNING_PEAK >= 23000) %>%
  tm_shape() + 
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)+
    tm_layout(main.title = "Flow for Passenger Volume more than or equals to 23000",
            main.title.size = 0.9,
            main.title.position = "center")

5 Computing Distance Matrix

In spatial interaction, a distance matrix is a table that shows the distance between pairs of locations. We will compute a distance matrix using the sgmap which is the hexagon grid of mpsz.

First we will use as.Spatial() to convert sgmap from sf tibble dataframe to Spatial Polygons Dataframe using sp package.

Show the code
sgmap_sp <- as(sgmap, "Spatial")
sgmap_sp
class       : SpatialPolygonsDataFrame 
features    : 1945 
extent      : 2292.538, 57042.54, 15315.71, 50606.24  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 9
names       : grid_id, SG, BIZ_COUNT, FINSERV_COUNT, MRTEXIT_COUNT, BUSSTOPS_COUNT, HDBCOMMERCIAL_COUNT, HDBRESIDENTIAL_COUNT, SCHOOLS_COUNT 
min values  :      33,  1,         0,             0,             0,              0,                   0,                    0,             0 
max values  :    3937, 11,       126,           176,            19,             20,                  27,                   75,             4 

Then we will use the spDist() function of sp package to compute the Euclidean distance between the centriods of the planning subzones.

Show the code
DIST <- spDists(sgmap_sp, 
                longlat = FALSE)

head(DIST, n=c(10,10))
          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
 [1,]    0.000 1299.038 2598.076 3897.114 5196.152  750.000 1984.313 3269.174
 [2,] 1299.038    0.000 1299.038 2598.076 3897.114  750.000  750.000 1984.313
 [3,] 2598.076 1299.038    0.000 1299.038 2598.076 1984.313  750.000  750.000
 [4,] 3897.114 2598.076 1299.038    0.000 1299.038 3269.174 1984.313  750.000
 [5,] 5196.152 3897.114 2598.076 1299.038    0.000 4562.072 3269.174 1984.313
 [6,]  750.000  750.000 1984.313 3269.174 4562.072    0.000 1299.038 2598.076
 [7,] 1984.313  750.000  750.000 1984.313 3269.174 1299.038    0.000 1299.038
 [8,] 3269.174 1984.313  750.000  750.000 1984.313 2598.076 1299.038    0.000
 [9,] 4562.072 3269.174 1984.313  750.000  750.000 3897.114 2598.076 1299.038
[10,] 5857.687 4562.072 3269.174 1984.313  750.000 5196.152 3897.114 2598.076
          [,9]    [,10]
 [1,] 4562.072 5857.687
 [2,] 3269.174 4562.072
 [3,] 1984.313 3269.174
 [4,]  750.000 1984.313
 [5,]  750.000  750.000
 [6,] 3897.114 5196.152
 [7,] 2598.076 3897.114
 [8,] 1299.038 2598.076
 [9,]    0.000 1299.038
[10,] 1299.038    0.000

5.1 Labelling Column and Row Headers of Distance Matrix

To label the column and row headers of the distance matrix DIST, we will first create a list sorted according to the distance matric by grid_id.

Show the code
hex_grid_id <- sgmap$grid_id

Then, we will attach the grid_id to the rows and columns of the distance matrix.

Show the code
colnames(DIST) <- paste0(hex_grid_id)
rownames(DIST) <- paste0(hex_grid_id)

head(DIST, n=c(10,10))
         33       34       35       36       37       60       61       62
33    0.000 1299.038 2598.076 3897.114 5196.152  750.000 1984.313 3269.174
34 1299.038    0.000 1299.038 2598.076 3897.114  750.000  750.000 1984.313
35 2598.076 1299.038    0.000 1299.038 2598.076 1984.313  750.000  750.000
36 3897.114 2598.076 1299.038    0.000 1299.038 3269.174 1984.313  750.000
37 5196.152 3897.114 2598.076 1299.038    0.000 4562.072 3269.174 1984.313
60  750.000  750.000 1984.313 3269.174 4562.072    0.000 1299.038 2598.076
61 1984.313  750.000  750.000 1984.313 3269.174 1299.038    0.000 1299.038
62 3269.174 1984.313  750.000  750.000 1984.313 2598.076 1299.038    0.000
63 4562.072 3269.174 1984.313  750.000  750.000 3897.114 2598.076 1299.038
64 5857.687 4562.072 3269.174 1984.313  750.000 5196.152 3897.114 2598.076
         63       64
33 4562.072 5857.687
34 3269.174 4562.072
35 1984.313 3269.174
36  750.000 1984.313
37  750.000  750.000
60 3897.114 5196.152
61 2598.076 3897.114
62 1299.038 2598.076
63    0.000 1299.038
64 1299.038    0.000

5.2 Pivoting Distance Value by Grid_ID

We will then pivot the distance matrix into a long table using the row and column grid_id as shown in the following code chunk.

Show the code
distpair <- melt(DIST) %>%
  rename(DISTANCE = value)

head(distpair, 10)
   Var1 Var2 DISTANCE
1    33   33    0.000
2    34   33 1299.038
3    35   33 2598.076
4    36   33 3897.114
5    37   33 5196.152
6    60   33  750.000
7    61   33 1984.313
8    62   33 3269.174
9    63   33 4562.072
10   64   33 5857.687

Notice that the within zone distance is 0.

5.3 Updating Intra-zonal Distances

To append a constant value to replace the intra-zonal distance of 0, we will select and find out the minimum value of the distance using summary().

Show the code
distpair %>%
  filter(DISTANCE > 0) %>%
  summary()
      Var1           Var2         DISTANCE    
 Min.   :  33   Min.   :  33   Min.   :  750  
 1st Qu.: 966   1st Qu.: 966   1st Qu.:10894  
 Median :1667   Median :1667   Median :17477  
 Mean   :1752   Mean   :1752   Mean   :18932  
 3rd Qu.:2420   3rd Qu.:2420   3rd Qu.:25401  
 Max.   :3937   Max.   :3937   Max.   :57862  

Next, we add a constant value of 300m, which is less than the minimum distance of 750m (from the above output) into intra-zones distance.

Show the code
distpair$DISTANCE <- ifelse(distpair$DISTANCE == 0,
                            300, distpair$DISTANCE)

distpair %>%
  summary()
      Var1           Var2         DISTANCE    
 Min.   :  33   Min.   :  33   Min.   :  300  
 1st Qu.: 966   1st Qu.: 966   1st Qu.:10894  
 Median :1667   Median :1667   Median :17477  
 Mean   :1752   Mean   :1752   Mean   :18923  
 3rd Qu.:2420   3rd Qu.:2420   3rd Qu.:25401  
 Max.   :3937   Max.   :3937   Max.   :57862  

We use the following code chunk to rename the origin and destination fields.

Show the code
distpair <- distpair %>%
  rename(orig = Var1,
         dest = Var2)

We will save the dataframe for future use.

write_rds(distpair, "data/rds/distpair.rds")

6 Preparing Flow Data

We will compute the total passenger trip between and within grid_ids by using the code chunk below. The output will have both intra and inter-grid flow data.

Show the code
flow_data <- od_data2 %>%
  rename(TRIPS = MORNING_PEAK )

head(flow_data, 10)
# A tibble: 10 × 21
# Groups:   ORIGIN_GRID_ID, DESTIN_GRID_ID [4]
   ORIGIN_GRID_ID DESTIN_GRID_ID TRIPS TORIGIN_BIZ_COUNT TORIGIN_FINSERV_COUNT
   <fct>          <fct>          <dbl>             <int>                 <int>
 1 664            664                9                 0                     2
 2 664            746               13                 0                     2
 3 664            746               13                 0                     2
 4 664            772              241                 0                     2
 5 664            772              241                 0                     2
 6 664            772              241                 0                     2
 7 664            772              241                 0                     2
 8 664            772              241                 0                     2
 9 664            772              241                 0                     2
10 664            799                1                 0                     2
# ℹ 16 more variables: TORIGIN_MRTEXIT_COUNT <int>,
#   TORIGIN_BUSSTOP_COUNT <int>, TORIGIN_HDBCOMMERCIAL_COUNT <int>,
#   TORIGIN_HDBRESIDENTIAL_COUNT <int>, TORIGIN_SCHOOLS_COUNT <int>,
#   TORIGIN_HDBCOMM_UNITS <dbl>, TORIGIN_HDBRES_UNITS <dbl>,
#   TDESTIN_BIZ_COUNT <int>, TDESTIN_FINSERV_COUNT <int>,
#   TDESTIN_MRTEXIT_COUNT <int>, TDESTIN_BUSSTOP_COUNT <int>,
#   TDESTIN_HDBCOMMERCIAL_COUNT <int>, TDESTIN_HDBRESIDENTIAL_COUNT <int>, …

Code chunk below is used to add three new fields in flow_data dataframe.

Show the code
flow_data$FlowNoIntra <- ifelse(
  flow_data$ORIGIN_GRID_ID == flow_data$DESTIN_GRID_ID, 
  0, flow_data$TRIPS)
flow_data$offset <- ifelse(
  flow_data$ORIGIN_GRID_ID == flow_data$DESTIN_GRID_ID, 
  0.000001, 1)

glimpse(flow_data)
Rows: 106,095
Columns: 23
Groups: ORIGIN_GRID_ID, DESTIN_GRID_ID [22,950]
$ ORIGIN_GRID_ID               <fct> 664, 664, 664, 664, 664, 664, 664, 664, 6…
$ DESTIN_GRID_ID               <fct> 664, 746, 746, 772, 772, 772, 772, 772, 7…
$ TRIPS                        <dbl> 9, 13, 13, 241, 241, 241, 241, 241, 241, …
$ TORIGIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_FINSERV_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7,…
$ TORIGIN_MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_BUSSTOP_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13…
$ TORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13…
$ TORIGIN_HDBRESIDENTIAL_COUNT <int> 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 45…
$ TORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,…
$ TORIGIN_HDBCOMM_UNITS        <dbl> 187, 187, 187, 187, 187, 187, 187, 187, 1…
$ TORIGIN_HDBRES_UNITS         <dbl> 699, 699, 699, 699, 699, 699, 699, 699, 6…
$ TDESTIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0,…
$ TDESTIN_FINSERV_COUNT        <int> 2, 0, 0, 7, 7, 7, 7, 7, 7, 0, 3, 3, 3, 7,…
$ TDESTIN_MRTEXIT_COUNT        <int> 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 5, 5, 5, 0,…
$ TDESTIN_BUSSTOP_COUNT        <int> 2, 9, 9, 20, 20, 20, 20, 20, 20, 9, 11, 1…
$ TDESTIN_HDBCOMMERCIAL_COUNT  <int> 2, 21, 21, 16, 16, 16, 16, 16, 16, 2, 4, …
$ TDESTIN_HDBRESIDENTIAL_COUNT <int> 8, 51, 51, 63, 63, 63, 63, 63, 63, 35, 56…
$ TDESTIN_SCHOOLS_COUNT        <int> 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3,…
$ TDESTIN_HDBCOMM_UNITS        <dbl> 187, 2032, 2032, 1278, 1278, 1278, 1278, …
$ TDESTIN_HDBRES_UNITS         <dbl> 699, 4079, 4079, 6643, 6643, 6643, 6643, …
$ FlowNoIntra                  <dbl> 0, 13, 13, 241, 241, 241, 241, 241, 241, …
$ offset                       <dbl> 1e-06, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00,…

Before we join the flow_data and dispair data, let us take a look at the distpair data.

Show the code
glimpse(distpair)
Rows: 3,783,025
Columns: 3
$ orig     <int> 33, 34, 35, 36, 37, 60, 61, 62, 63, 64, 87, 88, 89, 90, 91, 9…
$ dest     <int> 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 3…
$ DISTANCE <dbl> 300.000, 1299.038, 2598.076, 3897.114, 5196.152, 750.000, 198…

We need to convert the data value type of orgi and dest fields of distpair dataframe into factor data type. Otherwise, we would not be able to perform the left join.

Show the code
distpair$orig <- as.factor(distpair$orig)
distpair$dest <- as.factor(distpair$dest)

glimpse(distpair)
Rows: 3,783,025
Columns: 3
$ orig     <fct> 33, 34, 35, 36, 37, 60, 61, 62, 63, 64, 87, 88, 89, 90, 91, 9…
$ dest     <fct> 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 3…
$ DISTANCE <dbl> 300.000, 1299.038, 2598.076, 3897.114, 5196.152, 750.000, 198…

Now, left_join() of dplyr will be used to flow_data dataframe and distPair dataframe. The output is called flow_data1.

Show the code
flow_data1 <- flow_data %>%
  left_join (distpair,
             by = c("ORIGIN_GRID_ID" = "orig",
                    "DESTIN_GRID_ID" = "dest"))
glimpse(flow_data1)
Rows: 106,095
Columns: 24
Groups: ORIGIN_GRID_ID, DESTIN_GRID_ID [22,950]
$ ORIGIN_GRID_ID               <fct> 664, 664, 664, 664, 664, 664, 664, 664, 6…
$ DESTIN_GRID_ID               <fct> 664, 746, 746, 772, 772, 772, 772, 772, 7…
$ TRIPS                        <dbl> 9, 13, 13, 241, 241, 241, 241, 241, 241, …
$ TORIGIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_FINSERV_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7,…
$ TORIGIN_MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_BUSSTOP_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13…
$ TORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13…
$ TORIGIN_HDBRESIDENTIAL_COUNT <int> 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 45…
$ TORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,…
$ TORIGIN_HDBCOMM_UNITS        <dbl> 187, 187, 187, 187, 187, 187, 187, 187, 1…
$ TORIGIN_HDBRES_UNITS         <dbl> 699, 699, 699, 699, 699, 699, 699, 699, 6…
$ TDESTIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0,…
$ TDESTIN_FINSERV_COUNT        <int> 2, 0, 0, 7, 7, 7, 7, 7, 7, 0, 3, 3, 3, 7,…
$ TDESTIN_MRTEXIT_COUNT        <int> 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 5, 5, 5, 0,…
$ TDESTIN_BUSSTOP_COUNT        <int> 2, 9, 9, 20, 20, 20, 20, 20, 20, 9, 11, 1…
$ TDESTIN_HDBCOMMERCIAL_COUNT  <int> 2, 21, 21, 16, 16, 16, 16, 16, 16, 2, 4, …
$ TDESTIN_HDBRESIDENTIAL_COUNT <int> 8, 51, 51, 63, 63, 63, 63, 63, 63, 35, 56…
$ TDESTIN_SCHOOLS_COUNT        <int> 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3,…
$ TDESTIN_HDBCOMM_UNITS        <dbl> 187, 2032, 2032, 1278, 1278, 1278, 1278, …
$ TDESTIN_HDBRES_UNITS         <dbl> 699, 4079, 4079, 6643, 6643, 6643, 6643, …
$ FlowNoIntra                  <dbl> 0, 13, 13, 241, 241, 241, 241, 241, 241, …
$ offset                       <dbl> 1e-06, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00,…
$ DISTANCE                     <dbl> 300.000, 1299.038, 1299.038, 1500.000, 15…

We will filter out those intra-zonal flows using the FlowNoIntra column.

Show the code
inter_zonal_flow <- flow_data1 %>% 
  filter(FlowNoIntra > 0)

glimpse(inter_zonal_flow)
Rows: 101,715
Columns: 24
Groups: ORIGIN_GRID_ID, DESTIN_GRID_ID [22,619]
$ ORIGIN_GRID_ID               <fct> 664, 664, 664, 664, 664, 664, 664, 664, 6…
$ DESTIN_GRID_ID               <fct> 746, 746, 772, 772, 772, 772, 772, 772, 7…
$ TRIPS                        <dbl> 13, 13, 241, 241, 241, 241, 241, 241, 1, …
$ TORIGIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_FINSERV_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7,…
$ TORIGIN_MRTEXIT_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ TORIGIN_BUSSTOP_COUNT        <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13, 1…
$ TORIGIN_HDBCOMMERCIAL_COUNT  <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13, 1…
$ TORIGIN_HDBRESIDENTIAL_COUNT <int> 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 45, 4…
$ TORIGIN_SCHOOLS_COUNT        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3,…
$ TORIGIN_HDBCOMM_UNITS        <dbl> 187, 187, 187, 187, 187, 187, 187, 187, 1…
$ TORIGIN_HDBRES_UNITS         <dbl> 699, 699, 699, 699, 699, 699, 699, 699, 6…
$ TDESTIN_BIZ_COUNT            <int> 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 41, 4…
$ TDESTIN_FINSERV_COUNT        <int> 0, 0, 7, 7, 7, 7, 7, 7, 0, 3, 3, 3, 1, 1,…
$ TDESTIN_MRTEXIT_COUNT        <int> 0, 0, 2, 2, 2, 2, 2, 2, 0, 5, 5, 5, 0, 0,…
$ TDESTIN_BUSSTOP_COUNT        <int> 9, 9, 20, 20, 20, 20, 20, 20, 9, 11, 11, …
$ TDESTIN_HDBCOMMERCIAL_COUNT  <int> 21, 21, 16, 16, 16, 16, 16, 16, 2, 4, 4, …
$ TDESTIN_HDBRESIDENTIAL_COUNT <int> 51, 51, 63, 63, 63, 63, 63, 63, 35, 56, 5…
$ TDESTIN_SCHOOLS_COUNT        <int> 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 0, 0,…
$ TDESTIN_HDBCOMM_UNITS        <dbl> 2032, 2032, 1278, 1278, 1278, 1278, 1278,…
$ TDESTIN_HDBRES_UNITS         <dbl> 4079, 4079, 6643, 6643, 6643, 6643, 6643,…
$ FlowNoIntra                  <dbl> 13, 13, 241, 241, 241, 241, 241, 241, 1, …
$ offset                       <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ DISTANCE                     <dbl> 1299.038, 1299.038, 1500.000, 1500.000, 1…

Since Poisson Regression is based of log and log 0 is undefined, it is important for us to ensure that no 0 values in the explanatory variables.

In the code chunk below, summary() of Base R is used to compute the summary statistics of all variables in inter_zonal_flow data frame.

Show the code
summary(inter_zonal_flow)
 ORIGIN_GRID_ID  DESTIN_GRID_ID      TRIPS       TORIGIN_BIZ_COUNT
 2314   : 1067   2010   : 1381   Min.   :    1   Min.   :  0.000  
 1990   : 1019   2038   : 1194   1st Qu.:   63   1st Qu.:  0.000  
 2177   :  924   2177   : 1012   Median :  300   Median :  0.000  
 1987   :  921   2314   : 1000   Mean   : 1826   Mean   :  4.668  
 2038   :  871   1990   :  931   3rd Qu.: 1297   3rd Qu.:  4.000  
 1123   :  793   1987   :  883   Max.   :87864   Max.   :126.000  
 (Other):96120   (Other):95314                                    
 TORIGIN_FINSERV_COUNT TORIGIN_MRTEXIT_COUNT TORIGIN_BUSSTOP_COUNT
 Min.   : 0.000        Min.   :0.000         Min.   : 1.000       
 1st Qu.: 2.000        1st Qu.:0.000         1st Qu.: 7.000       
 Median : 5.000        Median :0.000         Median : 9.000       
 Mean   : 8.677        Mean   :1.309         Mean   : 9.705       
 3rd Qu.:11.000        3rd Qu.:2.000         3rd Qu.:12.000       
 Max.   :53.000        Max.   :9.000         Max.   :20.000       
                                                                  
 TORIGIN_HDBCOMMERCIAL_COUNT TORIGIN_HDBRESIDENTIAL_COUNT TORIGIN_SCHOOLS_COUNT
 Min.   : 1.000              Min.   : 1.00                Min.   :0.0000       
 1st Qu.: 4.000              1st Qu.:14.00                1st Qu.:0.0000       
 Median : 7.000              Median :31.00                Median :1.0000       
 Mean   : 8.641              Mean   :31.15                Mean   :0.8801       
 3rd Qu.:12.000              3rd Qu.:44.00                3rd Qu.:1.0000       
 Max.   :27.000              Max.   :75.00                Max.   :4.0000       
                                                                               
 TORIGIN_HDBCOMM_UNITS TORIGIN_HDBRES_UNITS TDESTIN_BIZ_COUNT
 Min.   :   0.0        Min.   :   8         Min.   :  0.000  
 1st Qu.: 248.0        1st Qu.:1672         1st Qu.:  0.000  
 Median : 537.0        Median :3239         Median :  1.000  
 Mean   : 680.4        Mean   :3334         Mean   :  5.237  
 3rd Qu.: 960.0        3rd Qu.:4708         3rd Qu.:  5.000  
 Max.   :2453.0        Max.   :8324         Max.   :126.000  
                                                             
 TDESTIN_FINSERV_COUNT TDESTIN_MRTEXIT_COUNT TDESTIN_BUSSTOP_COUNT
 Min.   : 0.000        Min.   :0.0           Min.   : 1.000       
 1st Qu.: 2.000        1st Qu.:0.0           1st Qu.: 7.000       
 Median : 5.000        Median :0.0           Median : 9.000       
 Mean   : 9.421        Mean   :1.4           Mean   : 9.771       
 3rd Qu.:11.000        3rd Qu.:2.0           3rd Qu.:12.000       
 Max.   :53.000        Max.   :9.0           Max.   :20.000       
                                                                  
 TDESTIN_HDBCOMMERCIAL_COUNT TDESTIN_HDBRESIDENTIAL_COUNT TDESTIN_SCHOOLS_COUNT
 Min.   : 1.000              Min.   : 1.00                Min.   :0.0000       
 1st Qu.: 4.000              1st Qu.:13.00                1st Qu.:0.0000       
 Median : 7.000              Median :30.00                Median :1.0000       
 Mean   : 8.512              Mean   :30.24                Mean   :0.8505       
 3rd Qu.:12.000              3rd Qu.:43.00                3rd Qu.:1.0000       
 Max.   :27.000              Max.   :75.00                Max.   :4.0000       
                                                                               
 TDESTIN_HDBCOMM_UNITS TDESTIN_HDBRES_UNITS  FlowNoIntra        offset 
 Min.   :   0.0        Min.   :   8         Min.   :    1   Min.   :1  
 1st Qu.: 247.0        1st Qu.:1560         1st Qu.:   63   1st Qu.:1  
 Median : 522.0        Median :3213         Median :  300   Median :1  
 Mean   : 671.6        Mean   :3249         Mean   : 1826   Mean   :1  
 3rd Qu.: 957.0        3rd Qu.:4601         3rd Qu.: 1297   3rd Qu.:1  
 Max.   :2453.0        Max.   :8324         Max.   :87864   Max.   :1  
                                                                       
    DISTANCE    
 Min.   :  750  
 1st Qu.: 1500  
 Median : 3269  
 Mean   : 4498  
 3rd Qu.: 6408  
 Max.   :25200  
                

The print report above reveals that variables TORIGIN_BIZ_COUNT, TORIGIN_FINSERV_COUNT, TORIGIN_MRTEXIT_COUNT, TORIGIN_SCHOOLS_COUNT, TORIGIN_HDBCOMM_UNITS, TDESTIN_BIZ_COUNT, TDESTIN_FINSERV_COUNT, TDESTIN_MRTEXIT_COUNT,TDESTIN_SCHOOLS_COUNT, TDESTIN_HDBCOMM_UNITS consist of 0 values.

We will use the following code chunk to replace 0 values with 0.99.

Show the code
inter_zonal_flow$TORIGIN_BIZ_COUNT <- ifelse(
  inter_zonal_flow$TORIGIN_BIZ_COUNT == 0,
  0.99, inter_zonal_flow$TORIGIN_BIZ_COUNT)

inter_zonal_flow$TORIGIN_FINSERV_COUNT <- ifelse(
  inter_zonal_flow$TORIGIN_FINSERV_COUNT == 0,
  0.99, inter_zonal_flow$TORIGIN_FINSERV_COUNT)

inter_zonal_flow$TORIGIN_MRTEXIT_COUNT <- ifelse(
  inter_zonal_flow$TORIGIN_MRTEXIT_COUNT == 0,
  0.99, inter_zonal_flow$TORIGIN_MRTEXIT_COUNT)

inter_zonal_flow$TORIGIN_BUSSTOP_COUNT <- ifelse(
  inter_zonal_flow$TORIGIN_BUSSTOP_COUNT == 0, 
  0.99, inter_zonal_flow$TORIGIN_BUSSTOP_COUNT)

inter_zonal_flow$TORIGIN_HDBCOMMERCIAL_COUNT <- ifelse(
  inter_zonal_flow$TORIGIN_HDBCOMMERCIAL_COUNT == 0, 
  0.99, inter_zonal_flow$TORIGIN_HDBCOMMERCIAL_COUNT)

inter_zonal_flow$TORIGIN_HDBRESIDENTIAL_COUNT <- ifelse(
  inter_zonal_flow$TORIGIN_HDBRESIDENTIAL_COUNT == 0,
  0.99, inter_zonal_flow$TORIGIN_HDBRESIDENTIAL_COUNT)

inter_zonal_flow$TORIGIN_SCHOOLS_COUNT <- ifelse(
  inter_zonal_flow$TORIGIN_SCHOOLS_COUNT == 0,
  0.99, inter_zonal_flow$TORIGIN_SCHOOLS_COUNT)

inter_zonal_flow$TORIGIN_HDBCOMM_UNITS <- ifelse(
  inter_zonal_flow$TORIGIN_HDBCOMM_UNITS == 0,
  0.99, inter_zonal_flow$TORIGIN_HDBCOMM_UNITS)

inter_zonal_flow$TORIGIN_HDBRES_UNITS <- ifelse(
  inter_zonal_flow$TORIGIN_HDBRES_UNITS == 0, 
  0.99, inter_zonal_flow$TORIGIN_HDBRES_UNITS)

inter_zonal_flow$TDESTIN_BIZ_COUNT <- ifelse(
  inter_zonal_flow$TDESTIN_BIZ_COUNT == 0,
  0.99, inter_zonal_flow$TDESTIN_BIZ_COUNT)

inter_zonal_flow$TDESTIN_FINSERV_COUNT <- ifelse(
  inter_zonal_flow$TDESTIN_FINSERV_COUNT == 0,
  0.99, inter_zonal_flow$TDESTIN_FINSERV_COUNT)

inter_zonal_flow$TDESTIN_MRTEXIT_COUNT <- ifelse(
  inter_zonal_flow$TDESTIN_MRTEXIT_COUNT == 0,
  0.99, inter_zonal_flow$TDESTIN_MRTEXIT_COUNT)

inter_zonal_flow$TDESTIN_BUSSTOP_COUNT <- ifelse(
  inter_zonal_flow$TDESTIN_BUSSTOP_COUNT == 0,
  0.99, inter_zonal_flow$TDESTIN_BUSSTOP_COUNT)

inter_zonal_flow$TDESTIN_HDBCOMMERCIAL_COUNT <- ifelse(
  inter_zonal_flow$TDESTIN_HDBCOMMERCIAL_COUNT == 0, 
  0.99, inter_zonal_flow$TDESTIN_HDBCOMMERCIAL_COUNT)

inter_zonal_flow$TDESTIN_HDBRESIDENTIAL_COUNT <- ifelse(
  inter_zonal_flow$TDESTIN_HDBRESIDENTIAL_COUNT == 0,
  0.99, inter_zonal_flow$TDESTIN_HDBRESIDENTIAL_COUNT)

inter_zonal_flow$TDESTIN_SCHOOLS_COUNT <- ifelse(
  inter_zonal_flow$TDESTIN_SCHOOLS_COUNT == 0,
  0.99, inter_zonal_flow$TDESTIN_SCHOOLS_COUNT)

inter_zonal_flow$TDESTIN_HDBCOMM_UNITS <- ifelse(
  inter_zonal_flow$TDESTIN_HDBCOMM_UNITS == 0,
  0.99, inter_zonal_flow$TDESTIN_HDBCOMM_UNITS)

inter_zonal_flow$TDESTIN_HDBRES_UNITS <- ifelse(
  inter_zonal_flow$TDESTIN_HDBRES_UNITS == 0,
  0.99, inter_zonal_flow$TDESTIN_HDBRES_UNITS)

We run summary() again to confirm that the 0 values have been replaced with 0.99.

Show the code
summary(inter_zonal_flow)
 ORIGIN_GRID_ID  DESTIN_GRID_ID      TRIPS       TORIGIN_BIZ_COUNT
 2314   : 1067   2010   : 1381   Min.   :    1   Min.   :  0.990  
 1990   : 1019   2038   : 1194   1st Qu.:   63   1st Qu.:  0.990  
 2177   :  924   2177   : 1012   Median :  300   Median :  0.990  
 1987   :  921   2314   : 1000   Mean   : 1826   Mean   :  5.165  
 2038   :  871   1990   :  931   3rd Qu.: 1297   3rd Qu.:  4.000  
 1123   :  793   1987   :  883   Max.   :87864   Max.   :126.000  
 (Other):96120   (Other):95314                                    
 TORIGIN_FINSERV_COUNT TORIGIN_MRTEXIT_COUNT TORIGIN_BUSSTOP_COUNT
 Min.   : 0.990        Min.   :0.99          Min.   : 1.000       
 1st Qu.: 2.000        1st Qu.:0.99          1st Qu.: 7.000       
 Median : 5.000        Median :0.99          Median : 9.000       
 Mean   : 8.832        Mean   :1.87          Mean   : 9.705       
 3rd Qu.:11.000        3rd Qu.:2.00          3rd Qu.:12.000       
 Max.   :53.000        Max.   :9.00          Max.   :20.000       
                                                                  
 TORIGIN_HDBCOMMERCIAL_COUNT TORIGIN_HDBRESIDENTIAL_COUNT TORIGIN_SCHOOLS_COUNT
 Min.   : 1.000              Min.   : 1.00                Min.   :0.990        
 1st Qu.: 4.000              1st Qu.:14.00                1st Qu.:0.990        
 Median : 7.000              Median :31.00                Median :1.000        
 Mean   : 8.641              Mean   :31.15                Mean   :1.282        
 3rd Qu.:12.000              3rd Qu.:44.00                3rd Qu.:1.000        
 Max.   :27.000              Max.   :75.00                Max.   :4.000        
                                                                               
 TORIGIN_HDBCOMM_UNITS TORIGIN_HDBRES_UNITS TDESTIN_BIZ_COUNT
 Min.   :   0.99       Min.   :   8         Min.   :  0.990  
 1st Qu.: 248.00       1st Qu.:1672         1st Qu.:  0.990  
 Median : 537.00       Median :3239         Median :  1.000  
 Mean   : 680.48       Mean   :3334         Mean   :  5.714  
 3rd Qu.: 960.00       3rd Qu.:4708         3rd Qu.:  5.000  
 Max.   :2453.00       Max.   :8324         Max.   :126.000  
                                                             
 TDESTIN_FINSERV_COUNT TDESTIN_MRTEXIT_COUNT TDESTIN_BUSSTOP_COUNT
 Min.   : 0.990        Min.   :0.99          Min.   : 1.000       
 1st Qu.: 2.000        1st Qu.:0.99          1st Qu.: 7.000       
 Median : 5.000        Median :0.99          Median : 9.000       
 Mean   : 9.569        Mean   :1.95          Mean   : 9.771       
 3rd Qu.:11.000        3rd Qu.:2.00          3rd Qu.:12.000       
 Max.   :53.000        Max.   :9.00          Max.   :20.000       
                                                                  
 TDESTIN_HDBCOMMERCIAL_COUNT TDESTIN_HDBRESIDENTIAL_COUNT TDESTIN_SCHOOLS_COUNT
 Min.   : 1.000              Min.   : 1.00                Min.   :0.990        
 1st Qu.: 4.000              1st Qu.:13.00                1st Qu.:0.990        
 Median : 7.000              Median :30.00                Median :1.000        
 Mean   : 8.512              Mean   :30.24                Mean   :1.271        
 3rd Qu.:12.000              3rd Qu.:43.00                3rd Qu.:1.000        
 Max.   :27.000              Max.   :75.00                Max.   :4.000        
                                                                               
 TDESTIN_HDBCOMM_UNITS TDESTIN_HDBRES_UNITS  FlowNoIntra        offset 
 Min.   :   0.99       Min.   :   8         Min.   :    1   Min.   :1  
 1st Qu.: 247.00       1st Qu.:1560         1st Qu.:   63   1st Qu.:1  
 Median : 522.00       Median :3213         Median :  300   Median :1  
 Mean   : 671.62       Mean   :3249         Mean   : 1826   Mean   :1  
 3rd Qu.: 957.00       3rd Qu.:4601         3rd Qu.: 1297   3rd Qu.:1  
 Max.   :2453.00       Max.   :8324         Max.   :87864   Max.   :1  
                                                                       
    DISTANCE    
 Min.   :  750  
 1st Qu.: 1500  
 Median : 3269  
 Mean   : 4498  
 3rd Qu.: 6408  
 Max.   :25200  
                

7 Calibrating Spatial Interaction Models

Firstly, let us plot the distribution of the dependent variable (i.e. TRIPS) by using histogram method by using the code chunk below.

Show the code
ggplot(data=inter_zonal_flow,
       aes(x=TRIPS)) + 
  geom_histogram()

From the output, we observe that the distribution is highly skewed and does not resemble a normal distribution.

Next, let us visualise the relation between the dependent variable and one of the key independent variable in Spatial Interaction Model, namely distance.

Show the code
ggplot(data = inter_zonal_flow,
       aes(x = DISTANCE,
           y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

Again, their relationship hardly resemble linear relationship.

On the other hand, if we plot the scatter plot by using the log transformed version of both variables using the following code chunk, we can see that their relationship more resembles a linear relationship.

Show the code
ggplot(data = inter_zonal_flow,
       aes(x = log(DISTANCE),
           y = log(TRIPS))) +
  geom_point() +
  geom_smooth(method = lm)

For Spatial Interation Model, we will be using log transformed variables so that the relationship resembles a linear relationship and to handle the skewed distributions. We will also be using a poisson regression model because the dependent variable (Trips) cannot be negative.

Before we proceed to calibrate the spatial interaction models, we will write a function to calculate R-Squared value as shown below. The R-squared value measure how much variation of the trips can be accounted by the model.

CalcRSquared <- function(observed, estimated){
  r <- cor(observed, estimated)
  R2 <- r^2
  R2
}

7.1 Origin (Production) Constrained Spatial Interaction Model

An origin-constrained spatial interaction model estimates “where they went” using the information on how many people left a particular origin (i.e. origin grid_id in our case). This model can have variables that reflect characteristics of the destinations so it is useful in forecasting destination inflow totals that are unknown.

In reality, origin-constrained spatial interaction model is useful for policy makers when they come up with new bus routes and bus stops, and estimating how much resource they need to commit during peak hours and non peak hours (e.g. number of double-deck/ single deck buses to deploy during peak and non peak hours respectively). Being able to estimate and project such resources is important because this could help the transport ministry and transport operators determine how many buses and bus drivers they need at any one time.

The general equation for Origin-constrained Spatial Interaction Model is as follow. \[ \lambda{i}{j}= exp(k + \mu{i} + \alpha\ln W{j} - \beta \ln d{i}{j}) \] We use glm() of Base Stats to calibrate an origin-constrained spatial interaction model. the explanatory variables are the destination related variables (such as TDESTIN_BIZ_COUNT, TDESTIN_FINSERV_COUNT) and the distance between the origin and destination (i.e. DISTANCE).

orcSIM_Poisson <- glm(formula = TRIPS ~ 
                ORIGIN_GRID_ID +
                log(TDESTIN_BIZ_COUNT) +
                log(TDESTIN_FINSERV_COUNT) +
                  log(TDESTIN_MRTEXIT_COUNT) +
                  log(TDESTIN_BUSSTOP_COUNT) +
                  log(TDESTIN_HDBCOMMERCIAL_COUNT) +
                  log(TDESTIN_HDBRESIDENTIAL_COUNT) +
                  log(TDESTIN_HDBCOMM_UNITS) +
                  log(TDESTIN_HDBRES_UNITS) + 
                  log(TDESTIN_SCHOOLS_COUNT) + 
                log(DISTANCE) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
summary(orcSIM_Poisson)

Call:
glm(formula = TRIPS ~ ORIGIN_GRID_ID + log(TDESTIN_BIZ_COUNT) + 
    log(TDESTIN_FINSERV_COUNT) + log(TDESTIN_MRTEXIT_COUNT) + 
    log(TDESTIN_BUSSTOP_COUNT) + log(TDESTIN_HDBCOMMERCIAL_COUNT) + 
    log(TDESTIN_HDBRESIDENTIAL_COUNT) + log(TDESTIN_HDBCOMM_UNITS) + 
    log(TDESTIN_HDBRES_UNITS) + log(TDESTIN_SCHOOLS_COUNT) + 
    log(DISTANCE) - 1, family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                                    Estimate Std. Error  z value Pr(>|z|)    
ORIGIN_GRID_ID664                  1.541e+01  2.328e-02    662.0   <2e-16 ***
ORIGIN_GRID_ID718                  1.939e+01  2.169e-03   8940.1   <2e-16 ***
ORIGIN_GRID_ID745                  1.708e+01  3.088e-03   5532.1   <2e-16 ***
ORIGIN_GRID_ID746                  1.912e+01  2.220e-03   8612.4   <2e-16 ***
ORIGIN_GRID_ID772                  1.878e+01  2.088e-03   8991.7   <2e-16 ***
ORIGIN_GRID_ID799                  1.817e+01  2.811e-03   6464.3   <2e-16 ***
ORIGIN_GRID_ID800                  1.932e+01  2.108e-03   9167.4   <2e-16 ***
ORIGIN_GRID_ID826                  1.905e+01  2.100e-03   9072.5   <2e-16 ***
ORIGIN_GRID_ID827                  1.906e+01  2.282e-03   8353.2   <2e-16 ***
ORIGIN_GRID_ID854                  1.793e+01  2.668e-03   6720.6   <2e-16 ***
ORIGIN_GRID_ID880                  1.735e+01  3.263e-03   5316.7   <2e-16 ***
ORIGIN_GRID_ID881                  1.660e+01  6.231e-03   2663.9   <2e-16 ***
ORIGIN_GRID_ID908                  1.883e+01  2.164e-03   8700.8   <2e-16 ***
ORIGIN_GRID_ID934                  1.750e+01  2.779e-03   6298.9   <2e-16 ***
ORIGIN_GRID_ID935                  1.826e+01  2.352e-03   7764.4   <2e-16 ***
ORIGIN_GRID_ID961                  1.864e+01  2.347e-03   7942.0   <2e-16 ***
ORIGIN_GRID_ID962                  1.886e+01  2.185e-03   8633.4   <2e-16 ***
ORIGIN_GRID_ID987                  1.918e+01  2.194e-03   8742.9   <2e-16 ***
ORIGIN_GRID_ID988                  1.766e+01  2.825e-03   6252.2   <2e-16 ***
ORIGIN_GRID_ID989                  1.877e+01  2.168e-03   8659.7   <2e-16 ***
ORIGIN_GRID_ID1015                 1.759e+01  3.369e-03   5221.7   <2e-16 ***
ORIGIN_GRID_ID1016                 1.776e+01  2.485e-03   7147.6   <2e-16 ***
ORIGIN_GRID_ID1043                 1.800e+01  3.141e-03   5731.6   <2e-16 ***
ORIGIN_GRID_ID1068                 1.567e+01  1.920e-02    816.4   <2e-16 ***
ORIGIN_GRID_ID1070                 1.824e+01  2.341e-03   7788.8   <2e-16 ***
ORIGIN_GRID_ID1096                 1.777e+01  2.402e-03   7397.6   <2e-16 ***
ORIGIN_GRID_ID1097                 1.759e+01  2.988e-03   5887.3   <2e-16 ***
ORIGIN_GRID_ID1099                 1.907e+01  2.148e-03   8877.6   <2e-16 ***
ORIGIN_GRID_ID1122                 1.875e+01  2.266e-03   8275.6   <2e-16 ***
ORIGIN_GRID_ID1123                 1.843e+01  2.249e-03   8195.2   <2e-16 ***
ORIGIN_GRID_ID1124                 1.779e+01  2.619e-03   6793.4   <2e-16 ***
ORIGIN_GRID_ID1125                 1.839e+01  2.488e-03   7391.5   <2e-16 ***
ORIGIN_GRID_ID1127                 1.832e+01  2.174e-03   8425.9   <2e-16 ***
ORIGIN_GRID_ID1128                 1.818e+01  2.463e-03   7378.9   <2e-16 ***
ORIGIN_GRID_ID1148                 1.730e+01  3.230e-03   5357.0   <2e-16 ***
ORIGIN_GRID_ID1150                 1.868e+01  2.146e-03   8705.0   <2e-16 ***
ORIGIN_GRID_ID1151                 1.810e+01  2.365e-03   7653.3   <2e-16 ***
ORIGIN_GRID_ID1152                 1.830e+01  2.667e-03   6863.6   <2e-16 ***
ORIGIN_GRID_ID1153                 1.879e+01  2.236e-03   8404.8   <2e-16 ***
ORIGIN_GRID_ID1154                 1.886e+01  2.206e-03   8546.7   <2e-16 ***
ORIGIN_GRID_ID1155                 1.556e+01  1.048e-02   1485.1   <2e-16 ***
ORIGIN_GRID_ID1176                 1.757e+01  2.868e-03   6126.1   <2e-16 ***
ORIGIN_GRID_ID1178                 1.770e+01  2.446e-03   7235.5   <2e-16 ***
ORIGIN_GRID_ID1179                 1.741e+01  2.735e-03   6363.7   <2e-16 ***
ORIGIN_GRID_ID1180                 1.644e+01  5.684e-03   2892.4   <2e-16 ***
ORIGIN_GRID_ID1181                 1.752e+01  2.327e-03   7531.8   <2e-16 ***
ORIGIN_GRID_ID1182                 1.840e+01  2.173e-03   8466.3   <2e-16 ***
ORIGIN_GRID_ID1183                 1.905e+01  2.723e-03   6993.7   <2e-16 ***
ORIGIN_GRID_ID1205                 1.864e+01  2.167e-03   8601.6   <2e-16 ***
ORIGIN_GRID_ID1206                 1.776e+01  2.574e-03   6901.1   <2e-16 ***
ORIGIN_GRID_ID1207                 1.754e+01  3.066e-03   5721.1   <2e-16 ***
ORIGIN_GRID_ID1209                 1.796e+01  2.478e-03   7246.7   <2e-16 ***
ORIGIN_GRID_ID1232                 1.839e+01  2.240e-03   8213.4   <2e-16 ***
ORIGIN_GRID_ID1233                 1.780e+01  3.147e-03   5656.2   <2e-16 ***
ORIGIN_GRID_ID1235                 1.829e+01  2.462e-03   7426.7   <2e-16 ***
ORIGIN_GRID_ID1255                 1.692e+01  1.075e-02   1574.6   <2e-16 ***
ORIGIN_GRID_ID1258                 1.769e+01  3.323e-03   5323.9   <2e-16 ***
ORIGIN_GRID_ID1259                 1.790e+01  2.483e-03   7210.2   <2e-16 ***
ORIGIN_GRID_ID1261                 1.753e+01  2.576e-03   6804.2   <2e-16 ***
ORIGIN_GRID_ID1262                 1.846e+01  2.281e-03   8092.5   <2e-16 ***
ORIGIN_GRID_ID1283                 1.742e+01  3.085e-03   5644.3   <2e-16 ***
ORIGIN_GRID_ID1284                 1.799e+01  3.203e-03   5616.3   <2e-16 ***
ORIGIN_GRID_ID1286                 1.732e+01  4.037e-03   4290.5   <2e-16 ***
ORIGIN_GRID_ID1289                 1.770e+01  2.405e-03   7359.8   <2e-16 ***
ORIGIN_GRID_ID1309                 1.898e+01  2.403e-03   7901.2   <2e-16 ***
ORIGIN_GRID_ID1310                 1.869e+01  2.248e-03   8314.3   <2e-16 ***
ORIGIN_GRID_ID1315                 1.806e+01  2.333e-03   7740.3   <2e-16 ***
ORIGIN_GRID_ID1316                 1.692e+01  3.545e-03   4771.9   <2e-16 ***
ORIGIN_GRID_ID1337                 1.830e+01  2.349e-03   7790.0   <2e-16 ***
ORIGIN_GRID_ID1338                 1.787e+01  5.451e-03   3278.9   <2e-16 ***
ORIGIN_GRID_ID1343                 1.744e+01  2.629e-03   6633.5   <2e-16 ***
ORIGIN_GRID_ID1363                 1.756e+01  3.590e-03   4892.5   <2e-16 ***
ORIGIN_GRID_ID1364                 1.752e+01  2.842e-03   6165.5   <2e-16 ***
ORIGIN_GRID_ID1366                 1.771e+01  3.187e-03   5557.2   <2e-16 ***
ORIGIN_GRID_ID1369                 1.818e+01  2.243e-03   8106.8   <2e-16 ***
ORIGIN_GRID_ID1370                 1.849e+01  2.383e-03   7758.2   <2e-16 ***
ORIGIN_GRID_ID1374                 1.725e+01  3.229e-03   5341.8   <2e-16 ***
ORIGIN_GRID_ID1375                 1.853e+01  3.593e-03   5157.8   <2e-16 ***
ORIGIN_GRID_ID1391                 1.657e+01  5.067e-03   3270.1   <2e-16 ***
ORIGIN_GRID_ID1392                 1.687e+01  4.200e-03   4017.4   <2e-16 ***
ORIGIN_GRID_ID1396                 1.681e+01  6.142e-03   2737.0   <2e-16 ***
ORIGIN_GRID_ID1397                 1.723e+01  3.203e-03   5378.5   <2e-16 ***
ORIGIN_GRID_ID1401                 1.830e+01  2.463e-03   7429.4   <2e-16 ***
ORIGIN_GRID_ID1402                 1.888e+01  2.144e-03   8804.9   <2e-16 ***
ORIGIN_GRID_ID1423                 1.920e+01  6.145e-03   3123.8   <2e-16 ***
ORIGIN_GRID_ID1428                 1.843e+01  2.412e-03   7642.0   <2e-16 ***
ORIGIN_GRID_ID1429                 1.796e+01  3.514e-03   5110.4   <2e-16 ***
ORIGIN_GRID_ID1455                 1.727e+01  3.057e-03   5647.4   <2e-16 ***
ORIGIN_GRID_ID1456                 1.851e+01  2.235e-03   8282.7   <2e-16 ***
ORIGIN_GRID_ID1471                 1.798e+01  2.582e-03   6961.4   <2e-16 ***
ORIGIN_GRID_ID1482                 1.808e+01  2.347e-03   7700.9   <2e-16 ***
ORIGIN_GRID_ID1499                 1.797e+01  2.554e-03   7036.3   <2e-16 ***
ORIGIN_GRID_ID1509                 1.745e+01  3.742e-03   4663.6   <2e-16 ***
ORIGIN_GRID_ID1510                 1.911e+01  2.083e-03   9177.0   <2e-16 ***
ORIGIN_GRID_ID1525                 1.755e+01  2.738e-03   6409.9   <2e-16 ***
ORIGIN_GRID_ID1536                 1.794e+01  2.282e-03   7863.5   <2e-16 ***
ORIGIN_GRID_ID1537                 1.754e+01  3.896e-03   4501.4   <2e-16 ***
ORIGIN_GRID_ID1552                 1.427e+01  1.434e-02    995.3   <2e-16 ***
ORIGIN_GRID_ID1553                 1.670e+01  3.310e-03   5044.7   <2e-16 ***
ORIGIN_GRID_ID1563                 1.759e+01  3.532e-03   4980.4   <2e-16 ***
ORIGIN_GRID_ID1564                 1.903e+01  2.062e-03   9227.2   <2e-16 ***
ORIGIN_GRID_ID1578                 1.567e+01  7.329e-03   2138.4   <2e-16 ***
ORIGIN_GRID_ID1579                 1.801e+01  2.598e-03   6932.1   <2e-16 ***
ORIGIN_GRID_ID1590                 1.874e+01  2.136e-03   8776.0   <2e-16 ***
ORIGIN_GRID_ID1591                 1.907e+01  2.181e-03   8744.9   <2e-16 ***
ORIGIN_GRID_ID1605                 1.701e+01  3.163e-03   5376.8   <2e-16 ***
ORIGIN_GRID_ID1606                 1.701e+01  3.135e-03   5427.3   <2e-16 ***
ORIGIN_GRID_ID1617                 1.699e+01  5.937e-03   2861.1   <2e-16 ***
ORIGIN_GRID_ID1618                 1.875e+01  2.220e-03   8442.8   <2e-16 ***
ORIGIN_GRID_ID1631                 1.616e+01  5.372e-03   3007.2   <2e-16 ***
ORIGIN_GRID_ID1632                 1.759e+01  2.648e-03   6643.7   <2e-16 ***
ORIGIN_GRID_ID1634                 1.743e+01  4.023e-03   4332.1   <2e-16 ***
ORIGIN_GRID_ID1644                 1.763e+01  2.935e-03   6006.7   <2e-16 ***
ORIGIN_GRID_ID1645                 1.885e+01  2.221e-03   8487.3   <2e-16 ***
ORIGIN_GRID_ID1658                 1.818e+01  2.757e-03   6593.6   <2e-16 ***
ORIGIN_GRID_ID1659                 1.748e+01  2.643e-03   6613.0   <2e-16 ***
ORIGIN_GRID_ID1672                 1.767e+01  3.646e-03   4845.7   <2e-16 ***
ORIGIN_GRID_ID1684                 1.769e+01  2.954e-03   5986.2   <2e-16 ***
ORIGIN_GRID_ID1685                 1.684e+01  3.839e-03   4386.3   <2e-16 ***
ORIGIN_GRID_ID1686                 1.739e+01  2.764e-03   6290.8   <2e-16 ***
ORIGIN_GRID_ID1688                 1.500e+01  1.656e-02    905.6   <2e-16 ***
ORIGIN_GRID_ID1699                 1.712e+01  3.010e-03   5686.7   <2e-16 ***
ORIGIN_GRID_ID1700                 1.494e+01  2.252e-02    663.7   <2e-16 ***
ORIGIN_GRID_ID1712                 1.686e+01  3.884e-03   4340.5   <2e-16 ***
ORIGIN_GRID_ID1713                 1.811e+01  2.328e-03   7781.1   <2e-16 ***
ORIGIN_GRID_ID1727                 1.914e+01  2.112e-03   9064.5   <2e-16 ***
ORIGIN_GRID_ID1739                 1.734e+01  2.684e-03   6459.0   <2e-16 ***
ORIGIN_GRID_ID1753                 1.873e+01  2.206e-03   8490.4   <2e-16 ***
ORIGIN_GRID_ID1754                 1.803e+01  2.998e-03   6013.2   <2e-16 ***
ORIGIN_GRID_ID1766                 1.840e+01  2.296e-03   8015.6   <2e-16 ***
ORIGIN_GRID_ID1767                 1.774e+01  2.316e-03   7662.1   <2e-16 ***
ORIGIN_GRID_ID1780                 1.614e+01  5.977e-03   2700.1   <2e-16 ***
ORIGIN_GRID_ID1781                 1.798e+01  2.350e-03   7653.0   <2e-16 ***
ORIGIN_GRID_ID1792                 1.733e+01  2.957e-03   5861.8   <2e-16 ***
ORIGIN_GRID_ID1793                 1.797e+01  2.289e-03   7850.3   <2e-16 ***
ORIGIN_GRID_ID1794                 1.649e+01  3.934e-03   4192.7   <2e-16 ***
ORIGIN_GRID_ID1807                 1.754e+01  2.558e-03   6857.7   <2e-16 ***
ORIGIN_GRID_ID1820                 1.725e+01  3.045e-03   5665.6   <2e-16 ***
ORIGIN_GRID_ID1821                 1.851e+01  2.193e-03   8443.3   <2e-16 ***
ORIGIN_GRID_ID1833                 1.834e+01  2.121e-03   8648.6   <2e-16 ***
ORIGIN_GRID_ID1835                 1.797e+01  2.788e-03   6444.1   <2e-16 ***
ORIGIN_GRID_ID1847                 1.752e+01  4.115e-03   4257.8   <2e-16 ***
ORIGIN_GRID_ID1854                 1.649e+01  5.861e-03   2813.6   <2e-16 ***
ORIGIN_GRID_ID1859                 1.730e+01  2.333e-03   7415.3   <2e-16 ***
ORIGIN_GRID_ID1860                 1.776e+01  2.280e-03   7791.5   <2e-16 ***
ORIGIN_GRID_ID1861                 1.851e+01  2.448e-03   7563.8   <2e-16 ***
ORIGIN_GRID_ID1874                 1.696e+01  3.262e-03   5200.1   <2e-16 ***
ORIGIN_GRID_ID1875                 1.733e+01  2.539e-03   6827.9   <2e-16 ***
ORIGIN_GRID_ID1882                 1.787e+01  2.523e-03   7083.6   <2e-16 ***
ORIGIN_GRID_ID1883                 1.728e+01  3.638e-03   4748.8   <2e-16 ***
ORIGIN_GRID_ID1886                 1.854e+01  2.210e-03   8387.0   <2e-16 ***
ORIGIN_GRID_ID1887                 1.838e+01  2.156e-03   8525.9   <2e-16 ***
ORIGIN_GRID_ID1888                 1.755e+01  2.949e-03   5949.1   <2e-16 ***
ORIGIN_GRID_ID1905                 1.585e+01  4.867e-03   3256.3   <2e-16 ***
ORIGIN_GRID_ID1907                 1.732e+01  3.019e-03   5737.4   <2e-16 ***
ORIGIN_GRID_ID1908                 1.669e+01  3.782e-03   4412.7   <2e-16 ***
ORIGIN_GRID_ID1909                 1.795e+01  2.397e-03   7490.8   <2e-16 ***
ORIGIN_GRID_ID1912                 1.590e+01  8.652e-03   1838.0   <2e-16 ***
ORIGIN_GRID_ID1913                 1.721e+01  2.640e-03   6519.1   <2e-16 ***
ORIGIN_GRID_ID1914                 1.885e+01  2.127e-03   8862.0   <2e-16 ***
ORIGIN_GRID_ID1928                 1.616e+01  3.367e-03   4799.2   <2e-16 ***
ORIGIN_GRID_ID1929                 1.604e+01  4.392e-03   3651.3   <2e-16 ***
ORIGIN_GRID_ID1933                 1.697e+01  3.303e-03   5137.5   <2e-16 ***
ORIGIN_GRID_ID1935                 1.743e+01  2.952e-03   5904.1   <2e-16 ***
ORIGIN_GRID_ID1936                 1.779e+01  2.558e-03   6953.8   <2e-16 ***
ORIGIN_GRID_ID1937                 1.715e+01  3.176e-03   5400.6   <2e-16 ***
ORIGIN_GRID_ID1940                 1.897e+01  2.077e-03   9133.9   <2e-16 ***
ORIGIN_GRID_ID1941                 1.795e+01  2.379e-03   7546.2   <2e-16 ***
ORIGIN_GRID_ID1942                 1.754e+01  4.488e-03   3908.9   <2e-16 ***
ORIGIN_GRID_ID1955                 1.789e+01  2.538e-03   7050.6   <2e-16 ***
ORIGIN_GRID_ID1959                 1.754e+01  2.463e-03   7122.8   <2e-16 ***
ORIGIN_GRID_ID1960                 1.786e+01  2.390e-03   7473.1   <2e-16 ***
ORIGIN_GRID_ID1962                 1.758e+01  2.589e-03   6793.2   <2e-16 ***
ORIGIN_GRID_ID1963                 1.684e+01  2.779e-03   6059.1   <2e-16 ***
ORIGIN_GRID_ID1967                 1.910e+01  2.128e-03   8973.4   <2e-16 ***
ORIGIN_GRID_ID1968                 1.923e+01  2.220e-03   8662.2   <2e-16 ***
ORIGIN_GRID_ID1985                 1.610e+01  3.575e-03   4503.3   <2e-16 ***
ORIGIN_GRID_ID1987                 1.833e+01  2.201e-03   8329.1   <2e-16 ***
ORIGIN_GRID_ID1988                 1.685e+01  2.927e-03   5755.9   <2e-16 ***
ORIGIN_GRID_ID1989                 1.709e+01  2.964e-03   5763.7   <2e-16 ***
ORIGIN_GRID_ID1990                 1.884e+01  2.152e-03   8752.8   <2e-16 ***
ORIGIN_GRID_ID1994                 1.720e+01  5.479e-03   3138.2   <2e-16 ***
ORIGIN_GRID_ID1995                 1.938e+01  2.139e-03   9057.9   <2e-16 ***
ORIGIN_GRID_ID2010                 1.613e+01  2.924e-03   5516.0   <2e-16 ***
ORIGIN_GRID_ID2011                 1.720e+01  2.354e-03   7308.7   <2e-16 ***
ORIGIN_GRID_ID2012                 1.627e+01  4.111e-03   3958.1   <2e-16 ***
ORIGIN_GRID_ID2013                 1.714e+01  2.653e-03   6458.1   <2e-16 ***
ORIGIN_GRID_ID2014                 1.744e+01  2.483e-03   7023.1   <2e-16 ***
ORIGIN_GRID_ID2015                 1.743e+01  3.166e-03   5506.4   <2e-16 ***
ORIGIN_GRID_ID2016                 1.761e+01  2.505e-03   7032.6   <2e-16 ***
ORIGIN_GRID_ID2017                 1.762e+01  2.527e-03   6970.3   <2e-16 ***
ORIGIN_GRID_ID2021                 1.753e+01  3.718e-03   4714.2   <2e-16 ***
ORIGIN_GRID_ID2038                 1.645e+01  2.433e-03   6761.3   <2e-16 ***
ORIGIN_GRID_ID2039                 1.790e+01  2.730e-03   6556.7   <2e-16 ***
ORIGIN_GRID_ID2040                 1.810e+01  2.299e-03   7873.7   <2e-16 ***
ORIGIN_GRID_ID2041                 1.894e+01  2.171e-03   8722.8   <2e-16 ***
ORIGIN_GRID_ID2042                 1.739e+01  2.911e-03   5975.2   <2e-16 ***
ORIGIN_GRID_ID2043                 1.615e+01  5.185e-03   3114.9   <2e-16 ***
ORIGIN_GRID_ID2044                 1.864e+01  2.173e-03   8577.2   <2e-16 ***
ORIGIN_GRID_ID2064                 1.414e+01  9.049e-03   1562.5   <2e-16 ***
ORIGIN_GRID_ID2065                 1.635e+01  2.908e-03   5623.2   <2e-16 ***
ORIGIN_GRID_ID2066                 1.667e+01  2.904e-03   5740.2   <2e-16 ***
ORIGIN_GRID_ID2067                 1.800e+01  2.634e-03   6831.2   <2e-16 ***
ORIGIN_GRID_ID2068                 1.806e+01  2.598e-03   6949.3   <2e-16 ***
ORIGIN_GRID_ID2070                 1.815e+01  2.725e-03   6659.8   <2e-16 ***
ORIGIN_GRID_ID2071                 1.751e+01  3.316e-03   5280.0   <2e-16 ***
ORIGIN_GRID_ID2093                 1.664e+01  2.539e-03   6554.8   <2e-16 ***
ORIGIN_GRID_ID2094                 1.779e+01  2.759e-03   6448.0   <2e-16 ***
ORIGIN_GRID_ID2095                 1.842e+01  3.096e-03   5951.9   <2e-16 ***
ORIGIN_GRID_ID2098                 1.665e+01  4.381e-03   3799.9   <2e-16 ***
ORIGIN_GRID_ID2119                 1.710e+01  2.848e-03   6002.8   <2e-16 ***
ORIGIN_GRID_ID2120                 1.680e+01  3.099e-03   5421.8   <2e-16 ***
ORIGIN_GRID_ID2123                 1.728e+01  2.681e-03   6447.5   <2e-16 ***
ORIGIN_GRID_ID2147                 1.720e+01  2.542e-03   6765.9   <2e-16 ***
ORIGIN_GRID_ID2148                 1.818e+01  2.274e-03   7994.0   <2e-16 ***
ORIGIN_GRID_ID2149                 1.733e+01  3.158e-03   5489.0   <2e-16 ***
ORIGIN_GRID_ID2150                 1.596e+01  4.419e-03   3611.9   <2e-16 ***
ORIGIN_GRID_ID2151                 1.694e+01  3.037e-03   5575.6   <2e-16 ***
ORIGIN_GRID_ID2152                 1.788e+01  2.786e-03   6415.6   <2e-16 ***
ORIGIN_GRID_ID2154                 1.732e+01  3.362e-03   5150.7   <2e-16 ***
ORIGIN_GRID_ID2174                 1.668e+01  4.076e-03   4092.0   <2e-16 ***
ORIGIN_GRID_ID2177                 1.864e+01  2.158e-03   8636.3   <2e-16 ***
ORIGIN_GRID_ID2178                 1.772e+01  2.346e-03   7552.7   <2e-16 ***
ORIGIN_GRID_ID2179                 1.805e+01  2.532e-03   7127.3   <2e-16 ***
ORIGIN_GRID_ID2180                 1.784e+01  2.949e-03   6049.4   <2e-16 ***
ORIGIN_GRID_ID2201                 1.781e+01  2.454e-03   7254.9   <2e-16 ***
ORIGIN_GRID_ID2203                 1.753e+01  3.573e-03   4907.6   <2e-16 ***
ORIGIN_GRID_ID2204                 1.647e+01  3.630e-03   4538.1   <2e-16 ***
ORIGIN_GRID_ID2205                 1.697e+01  2.523e-03   6727.8   <2e-16 ***
ORIGIN_GRID_ID2206                 1.898e+01  2.111e-03   8992.0   <2e-16 ***
ORIGIN_GRID_ID2208                 1.844e+01  2.501e-03   7375.3   <2e-16 ***
ORIGIN_GRID_ID2228                 1.731e+01  2.648e-03   6537.7   <2e-16 ***
ORIGIN_GRID_ID2231                 1.737e+01  2.496e-03   6961.7   <2e-16 ***
ORIGIN_GRID_ID2233                 1.896e+01  2.100e-03   9028.2   <2e-16 ***
ORIGIN_GRID_ID2234                 1.528e+01  2.498e-02    611.7   <2e-16 ***
ORIGIN_GRID_ID2235                 1.514e+01  2.059e-02    735.1   <2e-16 ***
ORIGIN_GRID_ID2254                 1.617e+01  8.043e-03   2010.3   <2e-16 ***
ORIGIN_GRID_ID2255                 1.761e+01  2.736e-03   6435.7   <2e-16 ***
ORIGIN_GRID_ID2256                 1.722e+01  2.764e-03   6231.3   <2e-16 ***
ORIGIN_GRID_ID2257                 1.598e+01  1.237e-02   1291.8   <2e-16 ***
ORIGIN_GRID_ID2259                 1.621e+01  5.797e-03   2796.3   <2e-16 ***
ORIGIN_GRID_ID2260                 1.847e+01  2.236e-03   8260.6   <2e-16 ***
ORIGIN_GRID_ID2261                 1.867e+01  2.173e-03   8588.3   <2e-16 ***
ORIGIN_GRID_ID2262                 1.758e+01  3.157e-03   5567.7   <2e-16 ***
ORIGIN_GRID_ID2281                 1.754e+01  3.361e-03   5217.6   <2e-16 ***
ORIGIN_GRID_ID2282                 1.707e+01  3.081e-03   5539.2   <2e-16 ***
ORIGIN_GRID_ID2283                 1.771e+01  2.394e-03   7394.7   <2e-16 ***
ORIGIN_GRID_ID2285                 1.838e+01  2.259e-03   8136.5   <2e-16 ***
ORIGIN_GRID_ID2286                 1.710e+01  3.137e-03   5451.4   <2e-16 ***
ORIGIN_GRID_ID2287                 1.895e+01  2.079e-03   9117.0   <2e-16 ***
ORIGIN_GRID_ID2288                 1.667e+01  4.826e-03   3455.4   <2e-16 ***
ORIGIN_GRID_ID2310                 1.724e+01  2.660e-03   6480.0   <2e-16 ***
ORIGIN_GRID_ID2312                 1.537e+01  1.072e-02   1433.9   <2e-16 ***
ORIGIN_GRID_ID2313                 1.769e+01  2.401e-03   7366.7   <2e-16 ***
ORIGIN_GRID_ID2314                 1.817e+01  2.118e-03   8578.3   <2e-16 ***
ORIGIN_GRID_ID2315                 1.753e+01  2.563e-03   6839.1   <2e-16 ***
ORIGIN_GRID_ID2316                 1.865e+01  2.105e-03   8859.5   <2e-16 ***
ORIGIN_GRID_ID2335                 1.530e+01  1.088e-02   1406.0   <2e-16 ***
ORIGIN_GRID_ID2339                 1.756e+01  2.963e-03   5928.7   <2e-16 ***
ORIGIN_GRID_ID2340                 1.835e+01  2.182e-03   8410.0   <2e-16 ***
ORIGIN_GRID_ID2341                 1.799e+01  2.227e-03   8077.2   <2e-16 ***
ORIGIN_GRID_ID2342                 1.737e+01  2.364e-03   7349.2   <2e-16 ***
ORIGIN_GRID_ID2343                 1.750e+01  2.801e-03   6248.0   <2e-16 ***
ORIGIN_GRID_ID2363                 1.698e+01  3.675e-03   4621.5   <2e-16 ***
ORIGIN_GRID_ID2367                 1.743e+01  3.118e-03   5589.2   <2e-16 ***
ORIGIN_GRID_ID2368                 1.814e+01  2.338e-03   7760.1   <2e-16 ***
ORIGIN_GRID_ID2369                 1.772e+01  2.534e-03   6993.0   <2e-16 ***
ORIGIN_GRID_ID2370                 1.813e+01  2.199e-03   8246.3   <2e-16 ***
ORIGIN_GRID_ID2371                 1.819e+01  2.316e-03   7854.2   <2e-16 ***
ORIGIN_GRID_ID2390                 1.715e+01  3.124e-03   5491.0   <2e-16 ***
ORIGIN_GRID_ID2391                 1.715e+01  2.905e-03   5903.0   <2e-16 ***
ORIGIN_GRID_ID2394                 1.659e+01  4.680e-03   3545.2   <2e-16 ***
ORIGIN_GRID_ID2395                 1.860e+01  2.187e-03   8506.3   <2e-16 ***
ORIGIN_GRID_ID2396                 1.816e+01  2.146e-03   8463.6   <2e-16 ***
ORIGIN_GRID_ID2397                 1.731e+01  2.827e-03   6124.3   <2e-16 ***
ORIGIN_GRID_ID2398                 1.765e+01  2.852e-03   6190.7   <2e-16 ***
ORIGIN_GRID_ID2418                 1.722e+01  3.384e-03   5089.2   <2e-16 ***
ORIGIN_GRID_ID2419                 1.653e+01  4.299e-03   3845.8   <2e-16 ***
ORIGIN_GRID_ID2422                 1.712e+01  6.439e-03   2658.9   <2e-16 ***
ORIGIN_GRID_ID2423                 1.748e+01  2.904e-03   6019.1   <2e-16 ***
ORIGIN_GRID_ID2424                 1.846e+01  2.107e-03   8759.5   <2e-16 ***
ORIGIN_GRID_ID2425                 1.792e+01  2.318e-03   7729.1   <2e-16 ***
ORIGIN_GRID_ID2426                 1.723e+01  4.011e-03   4294.2   <2e-16 ***
ORIGIN_GRID_ID2443                 1.779e+01  2.675e-03   6651.5   <2e-16 ***
ORIGIN_GRID_ID2445                 1.798e+01  2.310e-03   7784.6   <2e-16 ***
ORIGIN_GRID_ID2449                 1.814e+01  3.379e-03   5367.2   <2e-16 ***
ORIGIN_GRID_ID2450                 1.796e+01  2.438e-03   7366.9   <2e-16 ***
ORIGIN_GRID_ID2451                 1.843e+01  2.177e-03   8465.2   <2e-16 ***
ORIGIN_GRID_ID2472                 1.578e+01  1.807e-02    873.7   <2e-16 ***
ORIGIN_GRID_ID2473                 1.778e+01  2.754e-03   6458.2   <2e-16 ***
ORIGIN_GRID_ID2478                 1.754e+01  2.606e-03   6732.8   <2e-16 ***
ORIGIN_GRID_ID2479                 1.629e+01  6.093e-03   2673.3   <2e-16 ***
ORIGIN_GRID_ID2497                 1.806e+01  2.461e-03   7338.3   <2e-16 ***
ORIGIN_GRID_ID2499                 1.827e+01  2.711e-03   6736.8   <2e-16 ***
ORIGIN_GRID_ID2505                 1.766e+01  2.722e-03   6490.1   <2e-16 ***
ORIGIN_GRID_ID2527                 1.813e+01  2.454e-03   7385.4   <2e-16 ***
ORIGIN_GRID_ID2532                 1.772e+01  2.927e-03   6052.4   <2e-16 ***
ORIGIN_GRID_ID2533                 1.800e+01  3.379e-03   5326.7   <2e-16 ***
ORIGIN_GRID_ID2551                 1.753e+01  3.274e-03   5355.0   <2e-16 ***
ORIGIN_GRID_ID2553                 1.763e+01  4.380e-03   4024.4   <2e-16 ***
ORIGIN_GRID_ID2554                 1.629e+01  6.478e-03   2514.6   <2e-16 ***
ORIGIN_GRID_ID2559                 1.772e+01  3.278e-03   5405.9   <2e-16 ***
ORIGIN_GRID_ID2580                 1.817e+01  2.505e-03   7254.6   <2e-16 ***
ORIGIN_GRID_ID2581                 1.739e+01  3.956e-03   4396.6   <2e-16 ***
ORIGIN_GRID_ID2607                 1.872e+01  2.208e-03   8478.0   <2e-16 ***
ORIGIN_GRID_ID2608                 1.706e+01  4.181e-03   4080.4   <2e-16 ***
ORIGIN_GRID_ID2634                 1.856e+01  2.339e-03   7934.2   <2e-16 ***
ORIGIN_GRID_ID2635                 1.864e+01  2.507e-03   7436.4   <2e-16 ***
ORIGIN_GRID_ID2636                 1.806e+01  2.686e-03   6723.1   <2e-16 ***
ORIGIN_GRID_ID2661                 1.809e+01  2.363e-03   7653.5   <2e-16 ***
ORIGIN_GRID_ID2663                 1.868e+01  2.107e-03   8865.7   <2e-16 ***
ORIGIN_GRID_ID2665                 1.773e+01  2.961e-03   5988.2   <2e-16 ***
ORIGIN_GRID_ID2688                 1.813e+01  2.437e-03   7438.5   <2e-16 ***
ORIGIN_GRID_ID2689                 1.812e+01  2.506e-03   7232.1   <2e-16 ***
ORIGIN_GRID_ID2690                 1.714e+01  2.922e-03   5866.2   <2e-16 ***
ORIGIN_GRID_ID2691                 1.881e+01  2.141e-03   8786.9   <2e-16 ***
ORIGIN_GRID_ID2693                 1.845e+01  2.288e-03   8062.3   <2e-16 ***
ORIGIN_GRID_ID2715                 1.864e+01  2.437e-03   7649.0   <2e-16 ***
ORIGIN_GRID_ID2717                 1.739e+01  2.372e-03   7331.4   <2e-16 ***
ORIGIN_GRID_ID2718                 1.789e+01  2.872e-03   6228.0   <2e-16 ***
ORIGIN_GRID_ID2719                 1.872e+01  2.080e-03   9000.4   <2e-16 ***
ORIGIN_GRID_ID2742                 1.791e+01  2.794e-03   6409.6   <2e-16 ***
ORIGIN_GRID_ID2743                 1.691e+01  5.284e-03   3200.1   <2e-16 ***
ORIGIN_GRID_ID2744                 1.769e+01  2.429e-03   7280.6   <2e-16 ***
ORIGIN_GRID_ID2745                 1.762e+01  2.329e-03   7564.0   <2e-16 ***
ORIGIN_GRID_ID2747                 1.765e+01  2.717e-03   6495.9   <2e-16 ***
ORIGIN_GRID_ID2768                 1.827e+01  2.667e-03   6852.0   <2e-16 ***
ORIGIN_GRID_ID2771                 1.837e+01  2.181e-03   8423.1   <2e-16 ***
ORIGIN_GRID_ID2773                 1.799e+01  2.363e-03   7613.8   <2e-16 ***
ORIGIN_GRID_ID2798                 1.713e+01  3.229e-03   5305.3   <2e-16 ***
ORIGIN_GRID_ID2799                 1.785e+01  2.240e-03   7968.5   <2e-16 ***
ORIGIN_GRID_ID2800                 1.792e+01  2.412e-03   7430.9   <2e-16 ***
ORIGIN_GRID_ID2824                 1.715e+01  3.173e-03   5405.4   <2e-16 ***
ORIGIN_GRID_ID2825                 1.792e+01  2.188e-03   8187.9   <2e-16 ***
ORIGIN_GRID_ID2826                 1.801e+01  2.625e-03   6859.6   <2e-16 ***
ORIGIN_GRID_ID2827                 1.826e+01  2.314e-03   7888.3   <2e-16 ***
ORIGIN_GRID_ID2852                 1.815e+01  2.390e-03   7595.9   <2e-16 ***
ORIGIN_GRID_ID2853                 1.811e+01  2.145e-03   8441.1   <2e-16 ***
ORIGIN_GRID_ID2854                 1.862e+01  2.153e-03   8647.5   <2e-16 ***
ORIGIN_GRID_ID2878                 1.754e+01  3.104e-03   5650.1   <2e-16 ***
ORIGIN_GRID_ID2879                 1.784e+01  2.457e-03   7259.9   <2e-16 ***
ORIGIN_GRID_ID2880                 1.783e+01  2.442e-03   7304.2   <2e-16 ***
ORIGIN_GRID_ID2881                 1.913e+01  2.190e-03   8732.7   <2e-16 ***
ORIGIN_GRID_ID2907                 1.787e+01  2.743e-03   6515.9   <2e-16 ***
ORIGIN_GRID_ID2908                 1.832e+01  2.395e-03   7648.7   <2e-16 ***
ORIGIN_GRID_ID2933                 1.600e+01  8.024e-03   1994.5   <2e-16 ***
ORIGIN_GRID_ID2934                 1.759e+01  2.882e-03   6104.5   <2e-16 ***
ORIGIN_GRID_ID3098                 1.735e+01  5.578e-03   3110.3   <2e-16 ***
log(TDESTIN_BIZ_COUNT)             4.295e-02  1.029e-04    417.6   <2e-16 ***
log(TDESTIN_FINSERV_COUNT)         2.343e-01  1.038e-04   2258.4   <2e-16 ***
log(TDESTIN_MRTEXIT_COUNT)         6.802e-01  1.498e-04   4541.9   <2e-16 ***
log(TDESTIN_BUSSTOP_COUNT)         7.413e-02  2.476e-04    299.4   <2e-16 ***
log(TDESTIN_HDBCOMMERCIAL_COUNT)   8.726e-02  1.962e-04    444.8   <2e-16 ***
log(TDESTIN_HDBRESIDENTIAL_COUNT)  1.289e-01  4.500e-04    286.4   <2e-16 ***
log(TDESTIN_HDBCOMM_UNITS)         8.755e-03  7.367e-05    118.8   <2e-16 ***
log(TDESTIN_HDBRES_UNITS)         -1.503e-01  3.806e-04   -394.9   <2e-16 ***
log(TDESTIN_SCHOOLS_COUNT)         3.309e-01  2.262e-04   1463.1   <2e-16 ***
log(DISTANCE)                     -1.474e+00  1.271e-04 -11601.0   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2954357158  on 101715  degrees of freedom
Residual deviance:  152730527  on 101357  degrees of freedom
AIC: 153489469

Number of Fisher Scoring iterations: 6

Based on the above output, all the destination related variables are significant because their p-values are less than 0.05. Based on the coefficients, the destination’s MRT Exits seemed to have the biggest influence on the spatial interaction as compared to other variables because it has the biggest coefficient (0.680174) amongst the other variables. The destination’s schools has the next highest coefficient of 0.330944. Distance has a negative coefficient of -1.474483. It means that as distance increased by log(l.474483), the interactions decreased. From the output, we observed that the destination HDB Residential Count has a positive coefficient of 0.128855 but the destination HDB Residential Dwelling units has a negative coefficient of -0.150316. It could mean that with HDB residential dwelling units increase, the number of interactions decrease (i.e. less commuter flows). We will calibrate the model in the next section by removing some variables.

We compute the R-squared of the Origin Constrained Spatial Interaction Model using the CalcRSquared function written earlier.

CalcRSquared(orcSIM_Poisson$data$TRIPS, orcSIM_Poisson$fitted.values)
[1] 0.6265569

The above output indicates that these variables explain for 62.65569% of the observed spatial interaction patterns.

7.2 Destination (Attraction) Constrained Spatial Interaction Model

We will now develop a Destination-constrained Spatial Interaction Model so that we can compare it with the Origin-constrained Spatial Interaction Model. The Destination-constrained Spatial Interaction Model can be used to forecast total outflows from origins. Such a situation could arise, for example, in forecasting the effects of locating a new industrial park in a certain region of Singapore. The number of people to be employed and the businesses to set up are known, the destination-constrained spatial interaction model can be used to forecast the demand for housing in the region that will result from the new employment.

The general equation for destination constrained spatial interaction model is as follow:

\[ \lambda{i}{j}= exp(k + \mu\ln V{i} + \alpha{i} - \beta \ln d{i}{j}) \]

decSIM_Poisson <- glm(formula = TRIPS ~ 
                DESTIN_GRID_ID +
                log(TORIGIN_BIZ_COUNT) +
                log(TORIGIN_FINSERV_COUNT) +
                  log(TORIGIN_MRTEXIT_COUNT) +
                  log(TORIGIN_BUSSTOP_COUNT) +
                  log(TORIGIN_HDBCOMMERCIAL_COUNT) +
                  log(TORIGIN_HDBRESIDENTIAL_COUNT) +
                  log(TORIGIN_HDBCOMM_UNITS) +
                  log(TORIGIN_HDBRES_UNITS) + 
                  log(TORIGIN_SCHOOLS_COUNT) + 
                log(DISTANCE) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
summary(decSIM_Poisson)

Call:
glm(formula = TRIPS ~ DESTIN_GRID_ID + log(TORIGIN_BIZ_COUNT) + 
    log(TORIGIN_FINSERV_COUNT) + log(TORIGIN_MRTEXIT_COUNT) + 
    log(TORIGIN_BUSSTOP_COUNT) + log(TORIGIN_HDBCOMMERCIAL_COUNT) + 
    log(TORIGIN_HDBRESIDENTIAL_COUNT) + log(TORIGIN_HDBCOMM_UNITS) + 
    log(TORIGIN_HDBRES_UNITS) + log(TORIGIN_SCHOOLS_COUNT) + 
    log(DISTANCE) - 1, family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                                    Estimate Std. Error    z value Pr(>|z|)    
DESTIN_GRID_ID664                  1.485e+01  4.828e-03   3076.975  < 2e-16 ***
DESTIN_GRID_ID718                  1.468e+01  2.477e-03   5927.699  < 2e-16 ***
DESTIN_GRID_ID745                  1.309e+01  3.426e-03   3820.366  < 2e-16 ***
DESTIN_GRID_ID746                  1.395e+01  2.817e-03   4951.311  < 2e-16 ***
DESTIN_GRID_ID772                  1.513e+01  2.198e-03   6879.733  < 2e-16 ***
DESTIN_GRID_ID799                  1.520e+01  2.383e-03   6379.194  < 2e-16 ***
DESTIN_GRID_ID800                  1.403e+01  2.465e-03   5689.985  < 2e-16 ***
DESTIN_GRID_ID826                  1.624e+01  2.173e-03   7473.459  < 2e-16 ***
DESTIN_GRID_ID827                  1.491e+01  2.620e-03   5691.977  < 2e-16 ***
DESTIN_GRID_ID854                  1.374e+01  3.021e-03   4546.334  < 2e-16 ***
DESTIN_GRID_ID880                  1.320e+01  3.920e-03   3366.788  < 2e-16 ***
DESTIN_GRID_ID881                  1.374e+01  3.909e-03   3514.466  < 2e-16 ***
DESTIN_GRID_ID908                  1.412e+01  2.601e-03   5429.021  < 2e-16 ***
DESTIN_GRID_ID934                  1.449e+01  2.538e-03   5709.309  < 2e-16 ***
DESTIN_GRID_ID935                  1.416e+01  2.757e-03   5134.937  < 2e-16 ***
DESTIN_GRID_ID961                  1.405e+01  2.939e-03   4779.058  < 2e-16 ***
DESTIN_GRID_ID962                  1.612e+01  2.183e-03   7385.117  < 2e-16 ***
DESTIN_GRID_ID987                  1.511e+01  2.394e-03   6312.731  < 2e-16 ***
DESTIN_GRID_ID988                  1.318e+01  3.766e-03   3500.073  < 2e-16 ***
DESTIN_GRID_ID989                  1.431e+01  2.619e-03   5465.241  < 2e-16 ***
DESTIN_GRID_ID1015                 1.186e+01  8.635e-03   1373.721  < 2e-16 ***
DESTIN_GRID_ID1016                 1.345e+01  3.056e-03   4402.993  < 2e-16 ***
DESTIN_GRID_ID1043                 1.409e+01  3.434e-03   4101.477  < 2e-16 ***
DESTIN_GRID_ID1068                 1.218e+01  2.071e-02    587.808  < 2e-16 ***
DESTIN_GRID_ID1070                 1.438e+01  2.506e-03   5739.042  < 2e-16 ***
DESTIN_GRID_ID1096                 1.398e+01  2.648e-03   5278.400  < 2e-16 ***
DESTIN_GRID_ID1097                 1.359e+01  3.362e-03   4040.314  < 2e-16 ***
DESTIN_GRID_ID1099                 1.422e+01  2.597e-03   5475.927  < 2e-16 ***
DESTIN_GRID_ID1122                 1.474e+01  2.935e-03   5020.962  < 2e-16 ***
DESTIN_GRID_ID1123                 1.570e+01  2.220e-03   7070.753  < 2e-16 ***
DESTIN_GRID_ID1124                 1.426e+01  2.635e-03   5412.161  < 2e-16 ***
DESTIN_GRID_ID1125                 1.357e+01  3.343e-03   4060.668  < 2e-16 ***
DESTIN_GRID_ID1127                 1.375e+01  2.773e-03   4959.245  < 2e-16 ***
DESTIN_GRID_ID1128                 1.443e+01  3.112e-03   4638.858  < 2e-16 ***
DESTIN_GRID_ID1148                 1.389e+01  3.551e-03   3912.594  < 2e-16 ***
DESTIN_GRID_ID1150                 1.432e+01  2.560e-03   5594.373  < 2e-16 ***
DESTIN_GRID_ID1151                 1.377e+01  2.807e-03   4904.796  < 2e-16 ***
DESTIN_GRID_ID1152                 1.347e+01  3.833e-03   3513.925  < 2e-16 ***
DESTIN_GRID_ID1153                 1.413e+01  2.663e-03   5306.961  < 2e-16 ***
DESTIN_GRID_ID1154                 1.580e+01  2.191e-03   7209.066  < 2e-16 ***
DESTIN_GRID_ID1155                 1.115e+01  1.733e-02    643.072  < 2e-16 ***
DESTIN_GRID_ID1176                 1.481e+01  2.568e-03   5767.980  < 2e-16 ***
DESTIN_GRID_ID1178                 1.369e+01  2.731e-03   5012.493  < 2e-16 ***
DESTIN_GRID_ID1179                 1.292e+01  3.641e-03   3547.472  < 2e-16 ***
DESTIN_GRID_ID1180                 1.139e+01  1.032e-02   1103.548  < 2e-16 ***
DESTIN_GRID_ID1181                 1.450e+01  2.379e-03   6092.099  < 2e-16 ***
DESTIN_GRID_ID1182                 1.401e+01  2.785e-03   5032.847  < 2e-16 ***
DESTIN_GRID_ID1183                 1.389e+01  5.273e-03   2635.031  < 2e-16 ***
DESTIN_GRID_ID1205                 1.531e+01  2.241e-03   6830.019  < 2e-16 ***
DESTIN_GRID_ID1206                 1.411e+01  2.790e-03   5057.970  < 2e-16 ***
DESTIN_GRID_ID1207                 1.392e+01  2.944e-03   4727.261  < 2e-16 ***
DESTIN_GRID_ID1209                 1.554e+01  2.293e-03   6777.083  < 2e-16 ***
DESTIN_GRID_ID1232                 1.453e+01  2.444e-03   5943.421  < 2e-16 ***
DESTIN_GRID_ID1233                 1.511e+01  2.677e-03   5645.982  < 2e-16 ***
DESTIN_GRID_ID1235                 1.486e+01  2.469e-03   6017.994  < 2e-16 ***
DESTIN_GRID_ID1255                 1.494e+01  5.876e-03   2542.030  < 2e-16 ***
DESTIN_GRID_ID1258                 1.527e+01  2.555e-03   5977.315  < 2e-16 ***
DESTIN_GRID_ID1259                 1.377e+01  3.142e-03   4382.128  < 2e-16 ***
DESTIN_GRID_ID1261                 1.364e+01  2.949e-03   4625.786  < 2e-16 ***
DESTIN_GRID_ID1262                 1.412e+01  2.654e-03   5319.461  < 2e-16 ***
DESTIN_GRID_ID1283                 1.393e+01  3.217e-03   4330.130  < 2e-16 ***
DESTIN_GRID_ID1284                 1.350e+01  4.945e-03   2730.385  < 2e-16 ***
DESTIN_GRID_ID1286                 1.286e+01  4.819e-03   2667.992  < 2e-16 ***
DESTIN_GRID_ID1289                 1.459e+01  2.326e-03   6273.350  < 2e-16 ***
DESTIN_GRID_ID1309                 1.511e+01  2.704e-03   5586.980  < 2e-16 ***
DESTIN_GRID_ID1310                 1.578e+01  2.280e-03   6920.152  < 2e-16 ***
DESTIN_GRID_ID1315                 1.535e+01  2.257e-03   6801.736  < 2e-16 ***
DESTIN_GRID_ID1316                 1.311e+01  4.025e-03   3256.355  < 2e-16 ***
DESTIN_GRID_ID1337                 1.409e+01  2.720e-03   5179.499  < 2e-16 ***
DESTIN_GRID_ID1338                 1.334e+01  6.054e-03   2202.812  < 2e-16 ***
DESTIN_GRID_ID1343                 1.312e+01  3.299e-03   3975.842  < 2e-16 ***
DESTIN_GRID_ID1363                 1.487e+01  2.967e-03   5009.796  < 2e-16 ***
DESTIN_GRID_ID1364                 1.364e+01  3.419e-03   3989.908  < 2e-16 ***
DESTIN_GRID_ID1366                 1.405e+01  3.268e-03   4298.738  < 2e-16 ***
DESTIN_GRID_ID1369                 1.420e+01  2.667e-03   5325.984  < 2e-16 ***
DESTIN_GRID_ID1370                 1.402e+01  2.851e-03   4917.140  < 2e-16 ***
DESTIN_GRID_ID1374                 1.339e+01  3.556e-03   3765.883  < 2e-16 ***
DESTIN_GRID_ID1375                 1.382e+01  5.838e-03   2367.056  < 2e-16 ***
DESTIN_GRID_ID1391                 1.374e+01  4.325e-03   3177.204  < 2e-16 ***
DESTIN_GRID_ID1392                 1.261e+01  6.735e-03   1871.914  < 2e-16 ***
DESTIN_GRID_ID1396                 1.245e+01  8.426e-03   1477.270  < 2e-16 ***
DESTIN_GRID_ID1397                 1.363e+01  3.047e-03   4473.472  < 2e-16 ***
DESTIN_GRID_ID1401                 1.522e+01  2.368e-03   6426.019  < 2e-16 ***
DESTIN_GRID_ID1402                 1.428e+01  2.606e-03   5481.428  < 2e-16 ***
DESTIN_GRID_ID1423                 1.375e+01  4.544e-03   3025.688  < 2e-16 ***
DESTIN_GRID_ID1428                 1.370e+01  3.085e-03   4440.621  < 2e-16 ***
DESTIN_GRID_ID1429                 1.437e+01  3.287e-03   4372.579  < 2e-16 ***
DESTIN_GRID_ID1455                 1.356e+01  3.120e-03   4347.233  < 2e-16 ***
DESTIN_GRID_ID1456                 1.384e+01  2.965e-03   4665.801  < 2e-16 ***
DESTIN_GRID_ID1471                 1.434e+01  3.392e-03   4228.263  < 2e-16 ***
DESTIN_GRID_ID1482                 1.518e+01  2.304e-03   6587.815  < 2e-16 ***
DESTIN_GRID_ID1499                 1.350e+01  4.937e-03   2734.974  < 2e-16 ***
DESTIN_GRID_ID1509                 1.305e+01  4.961e-03   2631.142  < 2e-16 ***
DESTIN_GRID_ID1510                 1.599e+01  2.181e-03   7331.138  < 2e-16 ***
DESTIN_GRID_ID1525                 1.488e+01  2.541e-03   5854.915  < 2e-16 ***
DESTIN_GRID_ID1536                 1.452e+01  2.364e-03   6142.978  < 2e-16 ***
DESTIN_GRID_ID1537                 1.462e+01  3.090e-03   4731.910  < 2e-16 ***
DESTIN_GRID_ID1552                 1.234e+01  9.550e-03   1292.145  < 2e-16 ***
DESTIN_GRID_ID1553                 1.374e+01  3.578e-03   3840.102  < 2e-16 ***
DESTIN_GRID_ID1563                 1.434e+01  2.865e-03   5004.244  < 2e-16 ***
DESTIN_GRID_ID1564                 1.436e+01  2.364e-03   6074.688  < 2e-16 ***
DESTIN_GRID_ID1578                 1.245e+01  6.532e-03   1906.243  < 2e-16 ***
DESTIN_GRID_ID1579                 1.461e+01  2.688e-03   5435.415  < 2e-16 ***
DESTIN_GRID_ID1590                 1.408e+01  2.600e-03   5413.418  < 2e-16 ***
DESTIN_GRID_ID1591                 1.451e+01  2.590e-03   5602.290  < 2e-16 ***
DESTIN_GRID_ID1605                 1.405e+01  2.956e-03   4752.897  < 2e-16 ***
DESTIN_GRID_ID1606                 1.401e+01  3.025e-03   4632.830  < 2e-16 ***
DESTIN_GRID_ID1617                 1.289e+01  6.705e-03   1922.147  < 2e-16 ***
DESTIN_GRID_ID1618                 1.589e+01  2.199e-03   7227.218  < 2e-16 ***
DESTIN_GRID_ID1631                 1.366e+01  3.566e-03   3832.123  < 2e-16 ***
DESTIN_GRID_ID1632                 1.377e+01  3.115e-03   4422.014  < 2e-16 ***
DESTIN_GRID_ID1634                 1.376e+01  4.714e-03   2919.579  < 2e-16 ***
DESTIN_GRID_ID1644                 1.415e+01  2.872e-03   4927.398  < 2e-16 ***
DESTIN_GRID_ID1645                 1.462e+01  2.531e-03   5775.135  < 2e-16 ***
DESTIN_GRID_ID1658                 1.360e+01  3.705e-03   3670.373  < 2e-16 ***
DESTIN_GRID_ID1659                 1.433e+01  2.576e-03   5562.743  < 2e-16 ***
DESTIN_GRID_ID1672                 1.408e+01  3.836e-03   3670.249  < 2e-16 ***
DESTIN_GRID_ID1684                 1.426e+01  2.934e-03   4859.903  < 2e-16 ***
DESTIN_GRID_ID1685                 1.396e+01  3.793e-03   3679.096  < 2e-16 ***
DESTIN_GRID_ID1686                 1.397e+01  2.954e-03   4729.710  < 2e-16 ***
DESTIN_GRID_ID1688                 1.343e+01  6.158e-03   2181.216  < 2e-16 ***
DESTIN_GRID_ID1699                 1.426e+01  2.682e-03   5316.594  < 2e-16 ***
DESTIN_GRID_ID1700                 1.382e+01  6.193e-03   2231.774  < 2e-16 ***
DESTIN_GRID_ID1712                 1.290e+01  4.307e-03   2995.056  < 2e-16 ***
DESTIN_GRID_ID1713                 1.472e+01  2.455e-03   5996.000  < 2e-16 ***
DESTIN_GRID_ID1727                 1.445e+01  2.527e-03   5718.111  < 2e-16 ***
DESTIN_GRID_ID1739                 1.482e+01  2.395e-03   6190.057  < 2e-16 ***
DESTIN_GRID_ID1753                 1.578e+01  2.192e-03   7196.946  < 2e-16 ***
DESTIN_GRID_ID1754                 1.393e+01  3.139e-03   4439.129  < 2e-16 ***
DESTIN_GRID_ID1766                 1.428e+01  2.571e-03   5554.592  < 2e-16 ***
DESTIN_GRID_ID1767                 1.427e+01  2.516e-03   5671.215  < 2e-16 ***
DESTIN_GRID_ID1780                 1.367e+01  1.017e-02   1344.909  < 2e-16 ***
DESTIN_GRID_ID1781                 1.398e+01  2.843e-03   4915.410  < 2e-16 ***
DESTIN_GRID_ID1792                 1.337e+01  3.463e-03   3860.905  < 2e-16 ***
DESTIN_GRID_ID1793                 1.453e+01  2.448e-03   5938.302  < 2e-16 ***
DESTIN_GRID_ID1794                 1.347e+01  3.913e-03   3441.428  < 2e-16 ***
DESTIN_GRID_ID1807                 1.276e+01  3.738e-03   3413.350  < 2e-16 ***
DESTIN_GRID_ID1820                 1.370e+01  3.221e-03   4253.892  < 2e-16 ***
DESTIN_GRID_ID1821                 1.523e+01  2.331e-03   6531.547  < 2e-16 ***
DESTIN_GRID_ID1833                 1.472e+01  2.306e-03   6383.110  < 2e-16 ***
DESTIN_GRID_ID1835                 1.307e+01  3.927e-03   3328.394  < 2e-16 ***
DESTIN_GRID_ID1847                 1.246e+01  9.380e-03   1328.835  < 2e-16 ***
DESTIN_GRID_ID1854                 1.380e+01  3.873e-03   3563.467  < 2e-16 ***
DESTIN_GRID_ID1859                 1.351e+01  2.648e-03   5101.234  < 2e-16 ***
DESTIN_GRID_ID1860                 1.376e+01  2.719e-03   5059.744  < 2e-16 ***
DESTIN_GRID_ID1861                 1.351e+01  3.805e-03   3550.708  < 2e-16 ***
DESTIN_GRID_ID1874                 1.404e+01  2.926e-03   4798.831  < 2e-16 ***
DESTIN_GRID_ID1875                 1.441e+01  2.549e-03   5654.655  < 2e-16 ***
DESTIN_GRID_ID1882                 1.462e+01  2.571e-03   5687.876  < 2e-16 ***
DESTIN_GRID_ID1883                 1.321e+01  4.100e-03   3222.457  < 2e-16 ***
DESTIN_GRID_ID1886                 1.600e+01  2.193e-03   7296.801  < 2e-16 ***
DESTIN_GRID_ID1887                 1.585e+01  2.159e-03   7342.180  < 2e-16 ***
DESTIN_GRID_ID1888                 1.361e+01  3.798e-03   3582.254  < 2e-16 ***
DESTIN_GRID_ID1905                 1.317e+01  4.261e-03   3091.504  < 2e-16 ***
DESTIN_GRID_ID1907                 1.406e+01  2.947e-03   4769.903  < 2e-16 ***
DESTIN_GRID_ID1908                 1.342e+01  3.597e-03   3730.051  < 2e-16 ***
DESTIN_GRID_ID1909                 1.381e+01  2.960e-03   4665.915  < 2e-16 ***
DESTIN_GRID_ID1912                 1.063e+01  2.104e-02    505.402  < 2e-16 ***
DESTIN_GRID_ID1913                 1.385e+01  2.613e-03   5301.372  < 2e-16 ***
DESTIN_GRID_ID1914                 1.453e+01  2.470e-03   5881.719  < 2e-16 ***
DESTIN_GRID_ID1928                 1.399e+01  3.392e-03   4124.304  < 2e-16 ***
DESTIN_GRID_ID1929                 1.394e+01  3.480e-03   4005.037  < 2e-16 ***
DESTIN_GRID_ID1933                 1.474e+01  2.573e-03   5727.125  < 2e-16 ***
DESTIN_GRID_ID1935                 1.414e+01  2.917e-03   4848.562  < 2e-16 ***
DESTIN_GRID_ID1936                 1.408e+01  2.894e-03   4864.103  < 2e-16 ***
DESTIN_GRID_ID1937                 1.401e+01  2.952e-03   4744.915  < 2e-16 ***
DESTIN_GRID_ID1940                 1.376e+01  2.777e-03   4954.332  < 2e-16 ***
DESTIN_GRID_ID1941                 1.301e+01  3.634e-03   3580.466  < 2e-16 ***
DESTIN_GRID_ID1942                 1.407e+01  4.815e-03   2921.648  < 2e-16 ***
DESTIN_GRID_ID1955                 1.480e+01  2.624e-03   5639.928  < 2e-16 ***
DESTIN_GRID_ID1959                 1.445e+01  2.622e-03   5513.403  < 2e-16 ***
DESTIN_GRID_ID1960                 1.474e+01  2.424e-03   6079.333  < 2e-16 ***
DESTIN_GRID_ID1962                 1.361e+01  3.051e-03   4459.836  < 2e-16 ***
DESTIN_GRID_ID1963                 1.353e+01  2.937e-03   4608.017  < 2e-16 ***
DESTIN_GRID_ID1967                 1.420e+01  2.621e-03   5418.681  < 2e-16 ***
DESTIN_GRID_ID1968                 1.423e+01  2.971e-03   4789.511  < 2e-16 ***
DESTIN_GRID_ID1985                 1.433e+01  3.130e-03   4577.808  < 2e-16 ***
DESTIN_GRID_ID1987                 1.547e+01  2.261e-03   6842.999  < 2e-16 ***
DESTIN_GRID_ID1988                 1.332e+01  3.183e-03   4185.518  < 2e-16 ***
DESTIN_GRID_ID1989                 1.317e+01  3.537e-03   3723.598  < 2e-16 ***
DESTIN_GRID_ID1990                 1.573e+01  2.231e-03   7051.842  < 2e-16 ***
DESTIN_GRID_ID1994                 1.170e+01  1.258e-02    930.114  < 2e-16 ***
DESTIN_GRID_ID1995                 1.368e+01  3.081e-03   4441.487  < 2e-16 ***
DESTIN_GRID_ID2010                 1.447e+01  2.497e-03   5793.489  < 2e-16 ***
DESTIN_GRID_ID2011                 1.449e+01  2.685e-03   5398.987  < 2e-16 ***
DESTIN_GRID_ID2012                 1.368e+01  3.610e-03   3787.907  < 2e-16 ***
DESTIN_GRID_ID2013                 1.378e+01  2.685e-03   5133.705  < 2e-16 ***
DESTIN_GRID_ID2014                 1.392e+01  2.592e-03   5369.856  < 2e-16 ***
DESTIN_GRID_ID2015                 1.430e+01  3.015e-03   4743.402  < 2e-16 ***
DESTIN_GRID_ID2016                 1.391e+01  2.758e-03   5043.522  < 2e-16 ***
DESTIN_GRID_ID2017                 1.397e+01  2.750e-03   5078.657  < 2e-16 ***
DESTIN_GRID_ID2021                 1.238e+01  6.666e-03   1856.887  < 2e-16 ***
DESTIN_GRID_ID2038                 1.515e+01  2.354e-03   6434.607  < 2e-16 ***
DESTIN_GRID_ID2039                 1.361e+01  3.597e-03   3782.882  < 2e-16 ***
DESTIN_GRID_ID2040                 1.381e+01  2.899e-03   4764.046  < 2e-16 ***
DESTIN_GRID_ID2041                 1.455e+01  2.477e-03   5873.271  < 2e-16 ***
DESTIN_GRID_ID2042                 1.350e+01  3.481e-03   3879.001  < 2e-16 ***
DESTIN_GRID_ID2043                 1.431e+01  2.936e-03   4875.306  < 2e-16 ***
DESTIN_GRID_ID2044                 1.422e+01  2.571e-03   5529.484  < 2e-16 ***
DESTIN_GRID_ID2064                 1.424e+01  3.052e-03   4665.020  < 2e-16 ***
DESTIN_GRID_ID2065                 1.403e+01  3.033e-03   4626.265  < 2e-16 ***
DESTIN_GRID_ID2066                 1.407e+01  2.601e-03   5408.408  < 2e-16 ***
DESTIN_GRID_ID2067                 1.341e+01  3.506e-03   3825.441  < 2e-16 ***
DESTIN_GRID_ID2068                 1.385e+01  3.095e-03   4473.929  < 2e-16 ***
DESTIN_GRID_ID2070                 1.433e+01  3.034e-03   4723.235  < 2e-16 ***
DESTIN_GRID_ID2071                 1.440e+01  2.787e-03   5166.163  < 2e-16 ***
DESTIN_GRID_ID2093                 1.441e+01  2.524e-03   5708.869  < 2e-16 ***
DESTIN_GRID_ID2094                 1.431e+01  2.691e-03   5317.290  < 2e-16 ***
DESTIN_GRID_ID2095                 1.421e+01  3.408e-03   4170.831  < 2e-16 ***
DESTIN_GRID_ID2098                 1.407e+01  3.222e-03   4366.159  < 2e-16 ***
DESTIN_GRID_ID2119                 1.416e+01  3.004e-03   4713.053  < 2e-16 ***
DESTIN_GRID_ID2120                 1.482e+01  2.600e-03   5701.919  < 2e-16 ***
DESTIN_GRID_ID2123                 1.322e+01  3.654e-03   3616.957  < 2e-16 ***
DESTIN_GRID_ID2147                 1.437e+01  2.632e-03   5462.032  < 2e-16 ***
DESTIN_GRID_ID2148                 1.410e+01  2.674e-03   5273.941  < 2e-16 ***
DESTIN_GRID_ID2149                 1.461e+01  2.828e-03   5165.883  < 2e-16 ***
DESTIN_GRID_ID2150                 1.234e+01  6.175e-03   1999.073  < 2e-16 ***
DESTIN_GRID_ID2151                 1.247e+01  5.400e-03   2309.904  < 2e-16 ***
DESTIN_GRID_ID2152                 1.486e+01  2.472e-03   6010.768  < 2e-16 ***
DESTIN_GRID_ID2154                 1.275e+01  4.899e-03   2602.014  < 2e-16 ***
DESTIN_GRID_ID2174                 1.273e+01  5.096e-03   2497.874  < 2e-16 ***
DESTIN_GRID_ID2177                 1.602e+01  2.163e-03   7408.782  < 2e-16 ***
DESTIN_GRID_ID2178                 1.306e+01  3.202e-03   4077.734  < 2e-16 ***
DESTIN_GRID_ID2179                 1.435e+01  2.599e-03   5519.948  < 2e-16 ***
DESTIN_GRID_ID2180                 1.338e+01  3.951e-03   3387.070  < 2e-16 ***
DESTIN_GRID_ID2201                 1.403e+01  2.910e-03   4821.164  < 2e-16 ***
DESTIN_GRID_ID2203                 1.389e+01  3.913e-03   3549.488  < 2e-16 ***
DESTIN_GRID_ID2204                 1.421e+01  2.887e-03   4923.374  < 2e-16 ***
DESTIN_GRID_ID2205                 1.351e+01  2.834e-03   4766.279  < 2e-16 ***
DESTIN_GRID_ID2206                 1.441e+01  2.379e-03   6057.329  < 2e-16 ***
DESTIN_GRID_ID2208                 1.388e+01  3.044e-03   4559.683  < 2e-16 ***
DESTIN_GRID_ID2228                 1.369e+01  3.129e-03   4376.840  < 2e-16 ***
DESTIN_GRID_ID2231                 1.380e+01  2.805e-03   4920.322  < 2e-16 ***
DESTIN_GRID_ID2233                 1.434e+01  2.347e-03   6112.138  < 2e-16 ***
DESTIN_GRID_ID2234                 8.246e+00  9.131e-02     90.306  < 2e-16 ***
DESTIN_GRID_ID2235                 1.139e+01  3.136e-02    363.234  < 2e-16 ***
DESTIN_GRID_ID2254                 1.405e+01  5.864e-03   2396.036  < 2e-16 ***
DESTIN_GRID_ID2255                 1.340e+01  4.364e-03   3071.070  < 2e-16 ***
DESTIN_GRID_ID2256                 1.377e+01  3.011e-03   4573.405  < 2e-16 ***
DESTIN_GRID_ID2257                 1.356e+01  7.890e-03   1718.272  < 2e-16 ***
DESTIN_GRID_ID2259                 1.301e+01  4.621e-03   2814.997  < 2e-16 ***
DESTIN_GRID_ID2260                 1.357e+01  2.721e-03   4985.412  < 2e-16 ***
DESTIN_GRID_ID2261                 1.360e+01  2.715e-03   5008.709  < 2e-16 ***
DESTIN_GRID_ID2262                 1.262e+01  5.125e-03   2463.475  < 2e-16 ***
DESTIN_GRID_ID2281                 1.360e+01  4.252e-03   3199.741  < 2e-16 ***
DESTIN_GRID_ID2282                 1.482e+01  2.495e-03   5939.540  < 2e-16 ***
DESTIN_GRID_ID2283                 1.358e+01  3.124e-03   4346.065  < 2e-16 ***
DESTIN_GRID_ID2285                 1.430e+01  2.651e-03   5392.838  < 2e-16 ***
DESTIN_GRID_ID2286                 1.344e+01  3.140e-03   4278.815  < 2e-16 ***
DESTIN_GRID_ID2287                 1.438e+01  2.261e-03   6358.560  < 2e-16 ***
DESTIN_GRID_ID2288                 1.198e+01  7.004e-03   1711.106  < 2e-16 ***
DESTIN_GRID_ID2310                 1.409e+01  2.690e-03   5238.934  < 2e-16 ***
DESTIN_GRID_ID2312                 1.305e+01  5.307e-03   2459.199  < 2e-16 ***
DESTIN_GRID_ID2313                 1.521e+01  2.277e-03   6680.696  < 2e-16 ***
DESTIN_GRID_ID2314                 1.522e+01  2.163e-03   7037.522  < 2e-16 ***
DESTIN_GRID_ID2315                 1.324e+01  3.048e-03   4344.803  < 2e-16 ***
DESTIN_GRID_ID2316                 1.393e+01  2.526e-03   5513.832  < 2e-16 ***
DESTIN_GRID_ID2335                 1.245e+01  1.365e-02    912.573  < 2e-16 ***
DESTIN_GRID_ID2339                 1.410e+01  2.993e-03   4712.574  < 2e-16 ***
DESTIN_GRID_ID2340                 1.394e+01  2.436e-03   5720.078  < 2e-16 ***
DESTIN_GRID_ID2341                 1.427e+01  2.302e-03   6201.395  < 2e-16 ***
DESTIN_GRID_ID2342                 1.310e+01  2.845e-03   4604.579  < 2e-16 ***
DESTIN_GRID_ID2343                 1.296e+01  4.130e-03   3137.485  < 2e-16 ***
DESTIN_GRID_ID2363                 1.326e+01  4.174e-03   3178.270  < 2e-16 ***
DESTIN_GRID_ID2367                 1.374e+01  3.521e-03   3901.632  < 2e-16 ***
DESTIN_GRID_ID2368                 1.387e+01  2.731e-03   5077.428  < 2e-16 ***
DESTIN_GRID_ID2369                 1.464e+01  2.373e-03   6169.643  < 2e-16 ***
DESTIN_GRID_ID2370                 1.551e+01  2.196e-03   7061.609  < 2e-16 ***
DESTIN_GRID_ID2371                 1.350e+01  3.043e-03   4434.809  < 2e-16 ***
DESTIN_GRID_ID2390                 1.480e+01  2.505e-03   5907.504  < 2e-16 ***
DESTIN_GRID_ID2391                 1.456e+01  2.587e-03   5628.563  < 2e-16 ***
DESTIN_GRID_ID2394                 1.227e+01  6.112e-03   2007.910  < 2e-16 ***
DESTIN_GRID_ID2395                 1.371e+01  2.622e-03   5228.452  < 2e-16 ***
DESTIN_GRID_ID2396                 1.380e+01  2.438e-03   5658.025  < 2e-16 ***
DESTIN_GRID_ID2397                 1.229e+01  5.788e-03   2123.066  < 2e-16 ***
DESTIN_GRID_ID2398                 1.306e+01  4.034e-03   3238.852  < 2e-16 ***
DESTIN_GRID_ID2418                 1.401e+01  3.224e-03   4346.199  < 2e-16 ***
DESTIN_GRID_ID2419                 1.459e+01  2.802e-03   5206.382  < 2e-16 ***
DESTIN_GRID_ID2422                 1.248e+01  9.245e-03   1349.613  < 2e-16 ***
DESTIN_GRID_ID2423                 1.288e+01  3.794e-03   3394.089  < 2e-16 ***
DESTIN_GRID_ID2424                 1.420e+01  2.414e-03   5884.590  < 2e-16 ***
DESTIN_GRID_ID2425                 1.547e+01  2.251e-03   6872.897  < 2e-16 ***
DESTIN_GRID_ID2426                 1.363e+01  4.690e-03   2905.605  < 2e-16 ***
DESTIN_GRID_ID2443                 1.484e+01  2.534e-03   5856.254  < 2e-16 ***
DESTIN_GRID_ID2445                 1.438e+01  2.604e-03   5523.426  < 2e-16 ***
DESTIN_GRID_ID2449                 1.273e+01  6.308e-03   2017.952  < 2e-16 ***
DESTIN_GRID_ID2450                 1.314e+01  3.136e-03   4191.421  < 2e-16 ***
DESTIN_GRID_ID2451                 1.447e+01  2.333e-03   6201.634  < 2e-16 ***
DESTIN_GRID_ID2472                 1.185e+01  1.628e-02    728.242  < 2e-16 ***
DESTIN_GRID_ID2473                 1.456e+01  2.837e-03   5133.121  < 2e-16 ***
DESTIN_GRID_ID2478                 1.336e+01  3.135e-03   4261.912  < 2e-16 ***
DESTIN_GRID_ID2479                 1.250e+01  7.903e-03   1582.040  < 2e-16 ***
DESTIN_GRID_ID2497                 1.412e+01  2.882e-03   4899.640  < 2e-16 ***
DESTIN_GRID_ID2499                 1.343e+01  4.126e-03   3255.053  < 2e-16 ***
DESTIN_GRID_ID2505                 1.366e+01  3.282e-03   4163.804  < 2e-16 ***
DESTIN_GRID_ID2527                 1.491e+01  2.442e-03   6103.725  < 2e-16 ***
DESTIN_GRID_ID2532                 1.273e+01  4.582e-03   2777.341  < 2e-16 ***
DESTIN_GRID_ID2533                 1.262e+01  6.617e-03   1906.683  < 2e-16 ***
DESTIN_GRID_ID2551                 1.402e+01  3.954e-03   3545.315  < 2e-16 ***
DESTIN_GRID_ID2553                 1.330e+01  5.890e-03   2258.544  < 2e-16 ***
DESTIN_GRID_ID2554                 1.251e+01  7.309e-03   1710.902  < 2e-16 ***
DESTIN_GRID_ID2559                 1.275e+01  5.987e-03   2130.402  < 2e-16 ***
DESTIN_GRID_ID2580                 1.431e+01  2.852e-03   5016.362  < 2e-16 ***
DESTIN_GRID_ID2581                 1.319e+01  5.270e-03   2503.197  < 2e-16 ***
DESTIN_GRID_ID2607                 1.387e+01  2.951e-03   4701.385  < 2e-16 ***
DESTIN_GRID_ID2608                 1.285e+01  5.676e-03   2263.693  < 2e-16 ***
DESTIN_GRID_ID2634                 1.594e+01  2.274e-03   7008.468  < 2e-16 ***
DESTIN_GRID_ID2635                 1.333e+01  3.963e-03   3364.719  < 2e-16 ***
DESTIN_GRID_ID2636                 1.412e+01  2.927e-03   4824.970  < 2e-16 ***
DESTIN_GRID_ID2661                 1.379e+01  2.823e-03   4885.916  < 2e-16 ***
DESTIN_GRID_ID2663                 1.433e+01  2.403e-03   5962.643  < 2e-16 ***
DESTIN_GRID_ID2665                 1.470e+01  2.541e-03   5787.318  < 2e-16 ***
DESTIN_GRID_ID2688                 1.395e+01  3.046e-03   4577.648  < 2e-16 ***
DESTIN_GRID_ID2689                 1.465e+01  2.515e-03   5825.540  < 2e-16 ***
DESTIN_GRID_ID2690                 1.423e+01  2.592e-03   5487.991  < 2e-16 ***
DESTIN_GRID_ID2691                 1.388e+01  2.592e-03   5355.538  < 2e-16 ***
DESTIN_GRID_ID2693                 1.424e+01  2.728e-03   5222.423  < 2e-16 ***
DESTIN_GRID_ID2715                 1.386e+01  3.289e-03   4212.311  < 2e-16 ***
DESTIN_GRID_ID2717                 1.398e+01  2.425e-03   5764.353  < 2e-16 ***
DESTIN_GRID_ID2718                 1.301e+01  4.209e-03   3089.996  < 2e-16 ***
DESTIN_GRID_ID2719                 1.409e+01  2.462e-03   5722.769  < 2e-16 ***
DESTIN_GRID_ID2742                 1.411e+01  2.943e-03   4795.010  < 2e-16 ***
DESTIN_GRID_ID2743                 1.397e+01  3.986e-03   3504.343  < 2e-16 ***
DESTIN_GRID_ID2744                 1.450e+01  2.439e-03   5943.719  < 2e-16 ***
DESTIN_GRID_ID2745                 1.425e+01  2.434e-03   5856.119  < 2e-16 ***
DESTIN_GRID_ID2747                 1.337e+01  3.451e-03   3874.627  < 2e-16 ***
DESTIN_GRID_ID2768                 1.414e+01  3.087e-03   4580.396  < 2e-16 ***
DESTIN_GRID_ID2771                 1.588e+01  2.157e-03   7363.012  < 2e-16 ***
DESTIN_GRID_ID2773                 1.327e+01  3.078e-03   4312.148  < 2e-16 ***
DESTIN_GRID_ID2798                 1.262e+01  4.665e-03   2705.535  < 2e-16 ***
DESTIN_GRID_ID2799                 1.353e+01  2.742e-03   4934.067  < 2e-16 ***
DESTIN_GRID_ID2800                 1.513e+01  2.195e-03   6895.348  < 2e-16 ***
DESTIN_GRID_ID2824                 1.495e+01  2.471e-03   6049.032  < 2e-16 ***
DESTIN_GRID_ID2825                 1.391e+01  2.463e-03   5646.872  < 2e-16 ***
DESTIN_GRID_ID2826                 1.329e+01  3.659e-03   3631.665  < 2e-16 ***
DESTIN_GRID_ID2827                 1.572e+01  2.144e-03   7330.487  < 2e-16 ***
DESTIN_GRID_ID2852                 1.343e+01  3.556e-03   3778.154  < 2e-16 ***
DESTIN_GRID_ID2853                 1.488e+01  2.189e-03   6797.920  < 2e-16 ***
DESTIN_GRID_ID2854                 1.422e+01  2.501e-03   5685.263  < 2e-16 ***
DESTIN_GRID_ID2878                 1.356e+01  3.490e-03   3885.313  < 2e-16 ***
DESTIN_GRID_ID2879                 1.366e+01  2.902e-03   4707.074  < 2e-16 ***
DESTIN_GRID_ID2880                 1.306e+01  3.441e-03   3794.371  < 2e-16 ***
DESTIN_GRID_ID2881                 1.400e+01  3.059e-03   4576.453  < 2e-16 ***
DESTIN_GRID_ID2907                 1.302e+01  4.407e-03   2955.264  < 2e-16 ***
DESTIN_GRID_ID2908                 1.430e+01  2.588e-03   5524.182  < 2e-16 ***
DESTIN_GRID_ID2933                 1.506e+01  3.111e-03   4838.628  < 2e-16 ***
DESTIN_GRID_ID2934                 1.345e+01  3.330e-03   4039.526  < 2e-16 ***
DESTIN_GRID_ID3098                 1.453e+01  3.702e-03   3923.882  < 2e-16 ***
log(TORIGIN_BIZ_COUNT)             9.232e-04  9.932e-05      9.295  < 2e-16 ***
log(TORIGIN_FINSERV_COUNT)         7.466e-02  9.535e-05    783.081  < 2e-16 ***
log(TORIGIN_MRTEXIT_COUNT)         4.337e-02  1.623e-04    267.229  < 2e-16 ***
log(TORIGIN_BUSSTOP_COUNT)         2.024e-01  2.485e-04    814.570  < 2e-16 ***
log(TORIGIN_HDBCOMMERCIAL_COUNT)  -3.164e-02  1.906e-04   -166.039  < 2e-16 ***
log(TORIGIN_HDBRESIDENTIAL_COUNT)  2.187e-01  4.292e-04    509.538  < 2e-16 ***
log(TORIGIN_HDBCOMM_UNITS)         5.064e-04  6.986e-05      7.250 4.18e-13 ***
log(TORIGIN_HDBRES_UNITS)          2.614e-01  3.802e-04    687.650  < 2e-16 ***
log(TORIGIN_SCHOOLS_COUNT)         1.354e-01  2.189e-04    618.748  < 2e-16 ***
log(DISTANCE)                     -1.392e+00  1.213e-04 -11468.829  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2954357158  on 101715  degrees of freedom
Residual deviance:  140215829  on 101357  degrees of freedom
AIC: 140974771

Number of Fisher Scoring iterations: 6
CalcRSquared(decSIM_Poisson$data$TRIPS, decSIM_Poisson$fitted.values)
[1] 0.5804407

7.3 Doubly constrained Model

The general formula of Doubly Constrained Spatial Interaction Model

\[ \lambda{i}{j}= exp(k + \mu{i} + \alpha{i} - \beta \ln d{i}{j}) \]

dbcSIM_Poisson <- glm(formula = TRIPS ~ 
                ORIGIN_GRID_ID + 
                DESTIN_GRID_ID +
                log(DISTANCE),
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
summary(dbcSIM_Poisson)

Call:
glm(formula = TRIPS ~ ORIGIN_GRID_ID + DESTIN_GRID_ID + log(DISTANCE), 
    family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                     Estimate Std. Error    z value Pr(>|z|)    
(Intercept)        16.1125642  0.0236170    682.245  < 2e-16 ***
ORIGIN_GRID_ID718   4.2633749  0.0232019    183.751  < 2e-16 ***
ORIGIN_GRID_ID745   1.7648468  0.0233087     75.716  < 2e-16 ***
ORIGIN_GRID_ID746   3.7529858  0.0232065    161.721  < 2e-16 ***
ORIGIN_GRID_ID772   3.0617900  0.0231996    131.976  < 2e-16 ***
ORIGIN_GRID_ID799   2.4843271  0.0232732    106.746  < 2e-16 ***
ORIGIN_GRID_ID800   3.6822895  0.0231965    158.743  < 2e-16 ***
ORIGIN_GRID_ID826   3.9616779  0.0231983    170.775  < 2e-16 ***
ORIGIN_GRID_ID827   3.6132465  0.0232149    155.643  < 2e-16 ***
ORIGIN_GRID_ID854   2.4434098  0.0232551    105.070  < 2e-16 ***
ORIGIN_GRID_ID880   1.6658760  0.0233312     71.401  < 2e-16 ***
ORIGIN_GRID_ID881   1.1719320  0.0239361     48.961  < 2e-16 ***
ORIGIN_GRID_ID908   3.4029672  0.0232088    146.624  < 2e-16 ***
ORIGIN_GRID_ID934   2.0374716  0.0232801     87.520  < 2e-16 ***
ORIGIN_GRID_ID935   2.7526252  0.0232306    118.491  < 2e-16 ***
ORIGIN_GRID_ID961   3.0852525  0.0232318    132.803  < 2e-16 ***
ORIGIN_GRID_ID962   3.7950192  0.0232183    163.449  < 2e-16 ***
ORIGIN_GRID_ID987   3.9234555  0.0232143    169.011  < 2e-16 ***
ORIGIN_GRID_ID988   2.0775934  0.0232853     89.223  < 2e-16 ***
ORIGIN_GRID_ID989   3.2940233  0.0232149    141.893  < 2e-16 ***
ORIGIN_GRID_ID1015  2.0264645  0.0233598     86.750  < 2e-16 ***
ORIGIN_GRID_ID1016  2.1806873  0.0232482     93.800  < 2e-16 ***
ORIGIN_GRID_ID1043  2.7233602  0.0233222    116.771  < 2e-16 ***
ORIGIN_GRID_ID1068 -0.0059253  0.0300501     -0.197 0.843686    
ORIGIN_GRID_ID1070  3.0417649  0.0232305    130.939  < 2e-16 ***
ORIGIN_GRID_ID1096  2.5310227  0.0232401    108.907  < 2e-16 ***
ORIGIN_GRID_ID1097  2.5051987  0.0233121    107.463  < 2e-16 ***
ORIGIN_GRID_ID1099  4.5266261  0.0232335    194.832  < 2e-16 ***
ORIGIN_GRID_ID1122  3.3904374  0.0232325    145.935  < 2e-16 ***
ORIGIN_GRID_ID1123  3.0750517  0.0232224    132.417  < 2e-16 ***
ORIGIN_GRID_ID1124  2.6884790  0.0232644    115.562  < 2e-16 ***
ORIGIN_GRID_ID1125  3.3692898  0.0232571    144.872  < 2e-16 ***
ORIGIN_GRID_ID1127  3.6248522  0.0232446    155.944  < 2e-16 ***
ORIGIN_GRID_ID1128  3.3628161  0.0232800    144.451  < 2e-16 ***
ORIGIN_GRID_ID1148  1.7672066  0.0233482     75.689  < 2e-16 ***
ORIGIN_GRID_ID1150  3.4870270  0.0232169    150.194  < 2e-16 ***
ORIGIN_GRID_ID1151  2.9182796  0.0232427    125.557  < 2e-16 ***
ORIGIN_GRID_ID1152  3.3245668  0.0232735    142.848  < 2e-16 ***
ORIGIN_GRID_ID1153  4.1756863  0.0232517    179.586  < 2e-16 ***
ORIGIN_GRID_ID1154  4.0253482  0.0232397    173.210  < 2e-16 ***
ORIGIN_GRID_ID1155  0.8246997  0.0254086     32.457  < 2e-16 ***
ORIGIN_GRID_ID1176  2.1912876  0.0232932     94.074  < 2e-16 ***
ORIGIN_GRID_ID1178  2.4010630  0.0232495    103.274  < 2e-16 ***
ORIGIN_GRID_ID1179  2.2145602  0.0232881     95.094  < 2e-16 ***
ORIGIN_GRID_ID1180  1.5077843  0.0238094     63.327  < 2e-16 ***
ORIGIN_GRID_ID1181  2.7959993  0.0232564    120.225  < 2e-16 ***
ORIGIN_GRID_ID1182  3.2302305  0.0232515    138.926  < 2e-16 ***
ORIGIN_GRID_ID1183  3.6317566  0.0233125    155.786  < 2e-16 ***
ORIGIN_GRID_ID1205  3.6432924  0.0232241    156.875  < 2e-16 ***
ORIGIN_GRID_ID1206  2.7560662  0.0232697    118.440  < 2e-16 ***
ORIGIN_GRID_ID1207  2.6604516  0.0233286    114.042  < 2e-16 ***
ORIGIN_GRID_ID1209  3.3744263  0.0232792    144.955  < 2e-16 ***
ORIGIN_GRID_ID1232  3.0134771  0.0232294    129.727  < 2e-16 ***
ORIGIN_GRID_ID1233  2.5781860  0.0233473    110.428  < 2e-16 ***
ORIGIN_GRID_ID1235  3.5453494  0.0232680    152.370  < 2e-16 ***
ORIGIN_GRID_ID1255  1.6845012  0.0254901     66.085  < 2e-16 ***
ORIGIN_GRID_ID1258  2.3864664  0.0233543    102.185  < 2e-16 ***
ORIGIN_GRID_ID1259  2.6849757  0.0232576    115.445  < 2e-16 ***
ORIGIN_GRID_ID1261  2.5993267  0.0232708    111.699  < 2e-16 ***
ORIGIN_GRID_ID1262  3.5408514  0.0232431    152.340  < 2e-16 ***
ORIGIN_GRID_ID1283  1.7905943  0.0233233     76.773  < 2e-16 ***
ORIGIN_GRID_ID1284  2.1991802  0.0233421     94.215  < 2e-16 ***
ORIGIN_GRID_ID1286  2.0101286  0.0234687     85.651  < 2e-16 ***
ORIGIN_GRID_ID1289  2.6741869  0.0232584    114.977  < 2e-16 ***
ORIGIN_GRID_ID1309  3.5788512  0.0232422    153.980  < 2e-16 ***
ORIGIN_GRID_ID1310  3.6040366  0.0232288    155.154  < 2e-16 ***
ORIGIN_GRID_ID1315  3.1176907  0.0232455    134.120  < 2e-16 ***
ORIGIN_GRID_ID1316  1.9991755  0.0234110     85.395  < 2e-16 ***
ORIGIN_GRID_ID1337  2.4754532  0.0232398    106.518  < 2e-16 ***
ORIGIN_GRID_ID1338  2.1648600  0.0237556     91.131  < 2e-16 ***
ORIGIN_GRID_ID1343  2.4927448  0.0232849    107.054  < 2e-16 ***
ORIGIN_GRID_ID1363  2.0333090  0.0233957     86.909  < 2e-16 ***
ORIGIN_GRID_ID1364  1.8825533  0.0232959     80.811  < 2e-16 ***
ORIGIN_GRID_ID1366  2.5281520  0.0233312    108.359  < 2e-16 ***
ORIGIN_GRID_ID1369  3.2429156  0.0232426    139.525  < 2e-16 ***
ORIGIN_GRID_ID1370  3.7602055  0.0232638    161.634  < 2e-16 ***
ORIGIN_GRID_ID1374  1.6441818  0.0233937     70.283  < 2e-16 ***
ORIGIN_GRID_ID1375  3.0965418  0.0234476    132.062  < 2e-16 ***
ORIGIN_GRID_ID1391  1.0111452  0.0236689     42.720  < 2e-16 ***
ORIGIN_GRID_ID1392  1.6274333  0.0234984     69.257  < 2e-16 ***
ORIGIN_GRID_ID1396  1.7869240  0.0239482     74.616  < 2e-16 ***
ORIGIN_GRID_ID1397  2.3105881  0.0233662     98.886  < 2e-16 ***
ORIGIN_GRID_ID1401  3.1388325  0.0232996    134.716  < 2e-16 ***
ORIGIN_GRID_ID1402  3.4001401  0.0232688    146.124  < 2e-16 ***
ORIGIN_GRID_ID1423  4.2519905  0.0239249    177.723  < 2e-16 ***
ORIGIN_GRID_ID1428  2.7191299  0.0232937    116.733  < 2e-16 ***
ORIGIN_GRID_ID1429  2.2456055  0.0234313     95.838  < 2e-16 ***
ORIGIN_GRID_ID1455  1.4985219  0.0233759     64.105  < 2e-16 ***
ORIGIN_GRID_ID1456  2.6472942  0.0232787    113.722  < 2e-16 ***
ORIGIN_GRID_ID1471  2.7950695  0.0232828    120.049  < 2e-16 ***
ORIGIN_GRID_ID1482  2.2919194  0.0232883     98.415  < 2e-16 ***
ORIGIN_GRID_ID1499  2.8509869  0.0232891    122.417  < 2e-16 ***
ORIGIN_GRID_ID1509  1.9389867  0.0234684     82.621  < 2e-16 ***
ORIGIN_GRID_ID1510  3.7764166  0.0232574    162.375  < 2e-16 ***
ORIGIN_GRID_ID1525  2.5106599  0.0232889    107.805  < 2e-16 ***
ORIGIN_GRID_ID1536  2.4395402  0.0232797    104.793  < 2e-16 ***
ORIGIN_GRID_ID1537  1.5066609  0.0234947     64.128  < 2e-16 ***
ORIGIN_GRID_ID1552 -0.8181267  0.0272329    -30.042  < 2e-16 ***
ORIGIN_GRID_ID1553  1.4324086  0.0233782     61.271  < 2e-16 ***
ORIGIN_GRID_ID1563  2.1279984  0.0234361     90.800  < 2e-16 ***
ORIGIN_GRID_ID1564  3.1681698  0.0232579    136.219  < 2e-16 ***
ORIGIN_GRID_ID1578  0.3759345  0.0242668     15.492  < 2e-16 ***
ORIGIN_GRID_ID1579  2.9591412  0.0232752    127.137  < 2e-16 ***
ORIGIN_GRID_ID1590  3.2437444  0.0232643    139.430  < 2e-16 ***
ORIGIN_GRID_ID1591  3.2662952  0.0232683    140.375  < 2e-16 ***
ORIGIN_GRID_ID1605  1.7030536  0.0233489     72.939  < 2e-16 ***
ORIGIN_GRID_ID1606  1.5007387  0.0233506     64.270  < 2e-16 ***
ORIGIN_GRID_ID1617  1.6670098  0.0239204     69.690  < 2e-16 ***
ORIGIN_GRID_ID1618  3.2061690  0.0232694    137.785  < 2e-16 ***
ORIGIN_GRID_ID1631  0.6410697  0.0237513     26.991  < 2e-16 ***
ORIGIN_GRID_ID1632  2.0281669  0.0232871     87.094  < 2e-16 ***
ORIGIN_GRID_ID1634  2.3524929  0.0234759    100.209  < 2e-16 ***
ORIGIN_GRID_ID1644  2.1330017  0.0233485     91.355  < 2e-16 ***
ORIGIN_GRID_ID1645  3.1067914  0.0232697    133.513  < 2e-16 ***
ORIGIN_GRID_ID1658  2.2872250  0.0233084     98.129  < 2e-16 ***
ORIGIN_GRID_ID1659  2.0180251  0.0232853     86.665  < 2e-16 ***
ORIGIN_GRID_ID1672  1.7790278  0.0234537     75.853  < 2e-16 ***
ORIGIN_GRID_ID1684  2.2193981  0.0233240     95.155  < 2e-16 ***
ORIGIN_GRID_ID1685  1.1269060  0.0234522     48.051  < 2e-16 ***
ORIGIN_GRID_ID1686  2.0512207  0.0233004     88.034  < 2e-16 ***
ORIGIN_GRID_ID1688 -0.2850933  0.0284489    -10.021  < 2e-16 ***
ORIGIN_GRID_ID1699  1.5754643  0.0233555     67.456  < 2e-16 ***
ORIGIN_GRID_ID1700 -0.6234412  0.0323011    -19.301  < 2e-16 ***
ORIGIN_GRID_ID1712  1.1127577  0.0234608     47.430  < 2e-16 ***
ORIGIN_GRID_ID1713  2.5070004  0.0232511    107.823  < 2e-16 ***
ORIGIN_GRID_ID1727  3.7063186  0.0232622    159.328  < 2e-16 ***
ORIGIN_GRID_ID1739  1.6721728  0.0232901     71.798  < 2e-16 ***
ORIGIN_GRID_ID1753  3.2562216  0.0232703    139.930  < 2e-16 ***
ORIGIN_GRID_ID1754  2.6163420  0.0233540    112.030  < 2e-16 ***
ORIGIN_GRID_ID1766  2.5529983  0.0232520    109.797  < 2e-16 ***
ORIGIN_GRID_ID1767  2.1105025  0.0232512     90.770  < 2e-16 ***
ORIGIN_GRID_ID1780  0.7608908  0.0239259     31.802  < 2e-16 ***
ORIGIN_GRID_ID1781  2.5972891  0.0232847    111.545  < 2e-16 ***
ORIGIN_GRID_ID1792  1.6598381  0.0233260     71.158  < 2e-16 ***
ORIGIN_GRID_ID1793  2.1823499  0.0232515     93.859  < 2e-16 ***
ORIGIN_GRID_ID1794  0.8845130  0.0234656     37.694  < 2e-16 ***
ORIGIN_GRID_ID1807  2.1589604  0.0233033     92.646  < 2e-16 ***
ORIGIN_GRID_ID1820  1.6874053  0.0233350     72.312  < 2e-16 ***
ORIGIN_GRID_ID1821  3.0519248  0.0232434    131.303  < 2e-16 ***
ORIGIN_GRID_ID1833  3.0698158  0.0232579    131.990  < 2e-16 ***
ORIGIN_GRID_ID1835  2.7033573  0.0233294    115.878  < 2e-16 ***
ORIGIN_GRID_ID1847  1.4353696  0.0235081     61.059  < 2e-16 ***
ORIGIN_GRID_ID1854  1.3187113  0.0238708     55.244  < 2e-16 ***
ORIGIN_GRID_ID1859  1.9305888  0.0232817     82.923  < 2e-16 ***
ORIGIN_GRID_ID1860  2.4729031  0.0232746    106.249  < 2e-16 ***
ORIGIN_GRID_ID1861  3.3077045  0.0232882    142.034  < 2e-16 ***
ORIGIN_GRID_ID1874  1.5434933  0.0233604     66.073  < 2e-16 ***
ORIGIN_GRID_ID1875  1.6215017  0.0232747     69.668  < 2e-16 ***
ORIGIN_GRID_ID1882  2.7150416  0.0232811    116.620  < 2e-16 ***
ORIGIN_GRID_ID1883  2.1317524  0.0234259     91.000  < 2e-16 ***
ORIGIN_GRID_ID1886  3.4356812  0.0232610    147.701  < 2e-16 ***
ORIGIN_GRID_ID1887  3.1760307  0.0232591    136.550  < 2e-16 ***
ORIGIN_GRID_ID1888  2.3067395  0.0233476     98.800  < 2e-16 ***
ORIGIN_GRID_ID1905  0.6153094  0.0236403     26.028  < 2e-16 ***
ORIGIN_GRID_ID1907  2.1896142  0.0233380     93.822  < 2e-16 ***
ORIGIN_GRID_ID1908  1.4735654  0.0234526     62.832  < 2e-16 ***
ORIGIN_GRID_ID1909  2.8446237  0.0232683    122.253  < 2e-16 ***
ORIGIN_GRID_ID1912  0.5320271  0.0247281     21.515  < 2e-16 ***
ORIGIN_GRID_ID1913  1.9310617  0.0233123     82.834  < 2e-16 ***
ORIGIN_GRID_ID1914  3.6051353  0.0232601    154.992  < 2e-16 ***
ORIGIN_GRID_ID1928  1.1758266  0.0233826     50.286  < 2e-16 ***
ORIGIN_GRID_ID1929  1.0256940  0.0235483     43.557  < 2e-16 ***
ORIGIN_GRID_ID1933  1.7390948  0.0233801     74.383  < 2e-16 ***
ORIGIN_GRID_ID1935  2.0910013  0.0233354     89.606  < 2e-16 ***
ORIGIN_GRID_ID1936  2.5094349  0.0232845    107.773  < 2e-16 ***
ORIGIN_GRID_ID1937  1.9568636  0.0233594     83.772  < 2e-16 ***
ORIGIN_GRID_ID1940  3.6859451  0.0232588    158.475  < 2e-16 ***
ORIGIN_GRID_ID1941  2.7634391  0.0232857    118.675  < 2e-16 ***
ORIGIN_GRID_ID1942  2.3484717  0.0235945     99.535  < 2e-16 ***
ORIGIN_GRID_ID1955  2.5392680  0.0232718    109.114  < 2e-16 ***
ORIGIN_GRID_ID1959  2.3540862  0.0232699    101.164  < 2e-16 ***
ORIGIN_GRID_ID1960  2.5575724  0.0232672    109.922  < 2e-16 ***
ORIGIN_GRID_ID1962  2.2359749  0.0232874     96.016  < 2e-16 ***
ORIGIN_GRID_ID1963  1.4164679  0.0233107     60.765  < 2e-16 ***
ORIGIN_GRID_ID1967  4.0017014  0.0232593    172.047  < 2e-16 ***
ORIGIN_GRID_ID1968  4.0609401  0.0232692    174.520  < 2e-16 ***
ORIGIN_GRID_ID1985  1.3184571  0.0234141     56.310  < 2e-16 ***
ORIGIN_GRID_ID1987  2.9371745  0.0232454    126.355  < 2e-16 ***
ORIGIN_GRID_ID1988  1.5704686  0.0233267     67.325  < 2e-16 ***
ORIGIN_GRID_ID1989  1.8301680  0.0233345     78.432  < 2e-16 ***
ORIGIN_GRID_ID1990  3.7826724  0.0232392    162.771  < 2e-16 ***
ORIGIN_GRID_ID1994  2.1303420  0.0238014     89.505  < 2e-16 ***
ORIGIN_GRID_ID1995  4.3041642  0.0232607    185.040  < 2e-16 ***
ORIGIN_GRID_ID2010  1.3281933  0.0233246     56.944  < 2e-16 ***
ORIGIN_GRID_ID2011  2.2697972  0.0232602     97.583  < 2e-16 ***
ORIGIN_GRID_ID2012  1.1671609  0.0235030     49.660  < 2e-16 ***
ORIGIN_GRID_ID2013  1.7534898  0.0232901     75.289  < 2e-16 ***
ORIGIN_GRID_ID2014  2.1571507  0.0232747     92.682  < 2e-16 ***
ORIGIN_GRID_ID2015  2.2567765  0.0233604     96.607  < 2e-16 ***
ORIGIN_GRID_ID2016  2.1579985  0.0232794     92.700  < 2e-16 ***
ORIGIN_GRID_ID2017  2.1209920  0.0232827     91.097  < 2e-16 ***
ORIGIN_GRID_ID2021  2.4365469  0.0234550    103.882  < 2e-16 ***
ORIGIN_GRID_ID2038  1.7947281  0.0232670     77.136  < 2e-16 ***
ORIGIN_GRID_ID2039  2.4686852  0.0233044    105.932  < 2e-16 ***
ORIGIN_GRID_ID2040  2.7863388  0.0232524    119.830  < 2e-16 ***
ORIGIN_GRID_ID2041  3.6940838  0.0232447    158.922  < 2e-16 ***
ORIGIN_GRID_ID2042  2.4543852  0.0233282    105.211  < 2e-16 ***
ORIGIN_GRID_ID2043  0.8088389  0.0237169     34.104  < 2e-16 ***
ORIGIN_GRID_ID2044  3.0634090  0.0232463    131.780  < 2e-16 ***
ORIGIN_GRID_ID2064 -0.6365948  0.0248444    -25.623  < 2e-16 ***
ORIGIN_GRID_ID2065  1.4312270  0.0233199     61.374  < 2e-16 ***
ORIGIN_GRID_ID2066  1.5175092  0.0233198     65.074  < 2e-16 ***
ORIGIN_GRID_ID2067  2.6021698  0.0232854    111.751  < 2e-16 ***
ORIGIN_GRID_ID2068  2.6709431  0.0232850    114.707  < 2e-16 ***
ORIGIN_GRID_ID2070  2.6515076  0.0233041    113.779  < 2e-16 ***
ORIGIN_GRID_ID2071  2.1529991  0.0233784     92.094  < 2e-16 ***
ORIGIN_GRID_ID2093  1.7696503  0.0232758     76.030  < 2e-16 ***
ORIGIN_GRID_ID2094  2.3490627  0.0233007    100.815  < 2e-16 ***
ORIGIN_GRID_ID2095  2.8957578  0.0233551    123.988  < 2e-16 ***
ORIGIN_GRID_ID2098  1.2424659  0.0235527     52.753  < 2e-16 ***
ORIGIN_GRID_ID2119  1.9041322  0.0233085     81.692  < 2e-16 ***
ORIGIN_GRID_ID2120  1.5563948  0.0233448     66.670  < 2e-16 ***
ORIGIN_GRID_ID2123  1.7304196  0.0232988     74.271  < 2e-16 ***
ORIGIN_GRID_ID2147  2.0184237  0.0232757     86.718  < 2e-16 ***
ORIGIN_GRID_ID2148  2.8891949  0.0232472    124.281  < 2e-16 ***
ORIGIN_GRID_ID2149  1.9867106  0.0233495     85.086  < 2e-16 ***
ORIGIN_GRID_ID2150  0.3766063  0.0235629     15.983  < 2e-16 ***
ORIGIN_GRID_ID2151  1.3421957  0.0233456     57.493  < 2e-16 ***
ORIGIN_GRID_ID2152  2.5587735  0.0233105    109.769  < 2e-16 ***
ORIGIN_GRID_ID2154  2.8419154  0.0233889    121.507  < 2e-16 ***
ORIGIN_GRID_ID2174  1.0600645  0.0234939     45.121  < 2e-16 ***
ORIGIN_GRID_ID2177  3.5191024  0.0232437    151.400  < 2e-16 ***
ORIGIN_GRID_ID2178  2.2622495  0.0232632     97.246  < 2e-16 ***
ORIGIN_GRID_ID2179  2.6283157  0.0232817    112.892  < 2e-16 ***
ORIGIN_GRID_ID2180  3.2211876  0.0233278    138.083  < 2e-16 ***
ORIGIN_GRID_ID2201  2.5852297  0.0232626    111.133  < 2e-16 ***
ORIGIN_GRID_ID2203  2.3343276  0.0234102     99.714  < 2e-16 ***
ORIGIN_GRID_ID2204  0.9643884  0.0234242     41.171  < 2e-16 ***
ORIGIN_GRID_ID2205  1.4188447  0.0232844     60.935  < 2e-16 ***
ORIGIN_GRID_ID2206  3.5825513  0.0232395    154.158  < 2e-16 ***
ORIGIN_GRID_ID2208  3.7498943  0.0232799    161.079  < 2e-16 ***
ORIGIN_GRID_ID2228  1.9725276  0.0232991     84.661  < 2e-16 ***
ORIGIN_GRID_ID2231  1.8709802  0.0232802     80.368  < 2e-16 ***
ORIGIN_GRID_ID2233  3.6774600  0.0232402    158.237  < 2e-16 ***
ORIGIN_GRID_ID2234 -0.2259856  0.0340527     -6.636 3.22e-11 ***
ORIGIN_GRID_ID2235  0.8323161  0.0309850     26.862  < 2e-16 ***
ORIGIN_GRID_ID2254  1.2368696  0.0245620     50.357  < 2e-16 ***
ORIGIN_GRID_ID2255  2.4482239  0.0232961    105.091  < 2e-16 ***
ORIGIN_GRID_ID2256  1.9763851  0.0233082     84.794  < 2e-16 ***
ORIGIN_GRID_ID2257  0.6817746  0.0262409     25.981  < 2e-16 ***
ORIGIN_GRID_ID2259  0.8698694  0.0238589     36.459  < 2e-16 ***
ORIGIN_GRID_ID2260  2.9113123  0.0232530    125.201  < 2e-16 ***
ORIGIN_GRID_ID2261  3.2397190  0.0232489    139.349  < 2e-16 ***
ORIGIN_GRID_ID2262  3.0960172  0.0233611    132.529  < 2e-16 ***
ORIGIN_GRID_ID2281  2.2587093  0.0233878     96.576  < 2e-16 ***
ORIGIN_GRID_ID2282  1.9152084  0.0233446     82.041  < 2e-16 ***
ORIGIN_GRID_ID2283  2.4864564  0.0232679    106.862  < 2e-16 ***
ORIGIN_GRID_ID2285  2.9099305  0.0232584    125.113  < 2e-16 ***
ORIGIN_GRID_ID2286  1.6279757  0.0233580     69.697  < 2e-16 ***
ORIGIN_GRID_ID2287  3.5374709  0.0232393    152.219  < 2e-16 ***
ORIGIN_GRID_ID2288  2.1034507  0.0236423     88.970  < 2e-16 ***
ORIGIN_GRID_ID2310  1.9061263  0.0232958     81.823  < 2e-16 ***
ORIGIN_GRID_ID2312 -0.0545135  0.0255062     -2.137 0.032577 *  
ORIGIN_GRID_ID2313  2.3884699  0.0232740    102.624  < 2e-16 ***
ORIGIN_GRID_ID2314  3.1070292  0.0232417    133.683  < 2e-16 ***
ORIGIN_GRID_ID2315  2.3241021  0.0232863     99.805  < 2e-16 ***
ORIGIN_GRID_ID2316  3.9733089  0.0232448    170.933  < 2e-16 ***
ORIGIN_GRID_ID2335  0.0981577  0.0255758      3.838 0.000124 ***
ORIGIN_GRID_ID2339  2.0965353  0.0233338     89.850  < 2e-16 ***
ORIGIN_GRID_ID2340  2.9593494  0.0232491    127.289  < 2e-16 ***
ORIGIN_GRID_ID2341  2.5911169  0.0232523    111.435  < 2e-16 ***
ORIGIN_GRID_ID2342  2.5573485  0.0232682    109.907  < 2e-16 ***
ORIGIN_GRID_ID2343  2.6782215  0.0233171    114.861  < 2e-16 ***
ORIGIN_GRID_ID2363  1.5915342  0.0234342     67.915  < 2e-16 ***
ORIGIN_GRID_ID2367  2.0747157  0.0233550     88.834  < 2e-16 ***
ORIGIN_GRID_ID2368  2.7486646  0.0232624    118.159  < 2e-16 ***
ORIGIN_GRID_ID2369  2.8419439  0.0232829    122.062  < 2e-16 ***
ORIGIN_GRID_ID2370  3.4648977  0.0232492    149.033  < 2e-16 ***
ORIGIN_GRID_ID2371  3.3012905  0.0232698    141.870  < 2e-16 ***
ORIGIN_GRID_ID2390  2.0503745  0.0233451     87.829  < 2e-16 ***
ORIGIN_GRID_ID2391  1.6765538  0.0233285     71.867  < 2e-16 ***
ORIGIN_GRID_ID2394  1.4214014  0.0236173     60.185  < 2e-16 ***
ORIGIN_GRID_ID2395  3.6637799  0.0232496    157.584  < 2e-16 ***
ORIGIN_GRID_ID2396  3.3834015  0.0232459    145.548  < 2e-16 ***
ORIGIN_GRID_ID2397  2.4823519  0.0233246    106.426  < 2e-16 ***
ORIGIN_GRID_ID2398  2.7108087  0.0233394    116.148  < 2e-16 ***
ORIGIN_GRID_ID2418  1.6690451  0.0233963     71.338  < 2e-16 ***
ORIGIN_GRID_ID2419  1.1631900  0.0235450     49.403  < 2e-16 ***
ORIGIN_GRID_ID2422  2.1607745  0.0240306     89.918  < 2e-16 ***
ORIGIN_GRID_ID2423  2.6476238  0.0233276    113.497  < 2e-16 ***
ORIGIN_GRID_ID2424  3.6854741  0.0232428    158.564  < 2e-16 ***
ORIGIN_GRID_ID2425  3.3763511  0.0232637    145.134  < 2e-16 ***
ORIGIN_GRID_ID2426  3.0150934  0.0235139    128.226  < 2e-16 ***
ORIGIN_GRID_ID2443  2.5603054  0.0232999    109.885  < 2e-16 ***
ORIGIN_GRID_ID2445  2.6654463  0.0232624    114.582  < 2e-16 ***
ORIGIN_GRID_ID2449  3.2802229  0.0233907    140.236  < 2e-16 ***
ORIGIN_GRID_ID2450  3.3311394  0.0232736    143.129  < 2e-16 ***
ORIGIN_GRID_ID2451  3.6855280  0.0232504    158.514  < 2e-16 ***
ORIGIN_GRID_ID2472  0.3253937  0.0293671     11.080  < 2e-16 ***
ORIGIN_GRID_ID2473  2.1956839  0.0233154     94.173  < 2e-16 ***
ORIGIN_GRID_ID2478  2.8114272  0.0232959    120.684  < 2e-16 ***
ORIGIN_GRID_ID2479  1.5458081  0.0239448     64.557  < 2e-16 ***
ORIGIN_GRID_ID2497  2.3653690  0.0232903    101.560  < 2e-16 ***
ORIGIN_GRID_ID2499  2.7168070  0.0233099    116.552  < 2e-16 ***
ORIGIN_GRID_ID2505  3.0403066  0.0233144    130.405  < 2e-16 ***
ORIGIN_GRID_ID2527  2.7578771  0.0232766    118.483  < 2e-16 ***
ORIGIN_GRID_ID2532  3.0422189  0.0233316    130.391  < 2e-16 ***
ORIGIN_GRID_ID2533  3.7669573  0.0234247    160.811  < 2e-16 ***
ORIGIN_GRID_ID2551  2.0681389  0.0233833     88.445  < 2e-16 ***
ORIGIN_GRID_ID2553  2.0431180  0.0235588     86.724  < 2e-16 ***
ORIGIN_GRID_ID2554  0.9004110  0.0240383     37.457  < 2e-16 ***
ORIGIN_GRID_ID2559  3.2214239  0.0233832    137.766  < 2e-16 ***
ORIGIN_GRID_ID2580  2.5167059  0.0232827    108.093  < 2e-16 ***
ORIGIN_GRID_ID2581  1.9913346  0.0234841     84.795  < 2e-16 ***
ORIGIN_GRID_ID2607  3.1084780  0.0232557    133.665  < 2e-16 ***
ORIGIN_GRID_ID2608  1.7086519  0.0235199     72.647  < 2e-16 ***
ORIGIN_GRID_ID2634  3.3023539  0.0232609    141.970  < 2e-16 ***
ORIGIN_GRID_ID2635  3.1432337  0.0232831    135.001  < 2e-16 ***
ORIGIN_GRID_ID2636  2.7443450  0.0233030    117.768  < 2e-16 ***
ORIGIN_GRID_ID2661  2.4894337  0.0232689    106.986  < 2e-16 ***
ORIGIN_GRID_ID2663  3.4055803  0.0232515    146.467  < 2e-16 ***
ORIGIN_GRID_ID2665  2.4197313  0.0233483    103.636  < 2e-16 ***
ORIGIN_GRID_ID2688  2.4900803  0.0232774    106.974  < 2e-16 ***
ORIGIN_GRID_ID2689  2.7058280  0.0232839    116.210  < 2e-16 ***
ORIGIN_GRID_ID2690  1.6513356  0.0233357     70.764  < 2e-16 ***
ORIGIN_GRID_ID2691  3.3951766  0.0232519    146.017  < 2e-16 ***
ORIGIN_GRID_ID2693  3.0043751  0.0232753    129.080  < 2e-16 ***
ORIGIN_GRID_ID2715  3.1540649  0.0232778    135.497  < 2e-16 ***
ORIGIN_GRID_ID2717  1.9065119  0.0232752     81.912  < 2e-16 ***
ORIGIN_GRID_ID2718  2.3835564  0.0233327    102.155  < 2e-16 ***
ORIGIN_GRID_ID2719  3.1398021  0.0232543    135.020  < 2e-16 ***
ORIGIN_GRID_ID2742  2.3849578  0.0233169    102.284  < 2e-16 ***
ORIGIN_GRID_ID2743  1.4954291  0.0237490     62.968  < 2e-16 ***
ORIGIN_GRID_ID2744  2.2824259  0.0232779     98.051  < 2e-16 ***
ORIGIN_GRID_ID2745  2.1625209  0.0232711     92.927  < 2e-16 ***
ORIGIN_GRID_ID2747  2.0698599  0.0233229     88.748  < 2e-16 ***
ORIGIN_GRID_ID2768  2.7648499  0.0232977    118.675  < 2e-16 ***
ORIGIN_GRID_ID2771  3.0307035  0.0232557    130.321  < 2e-16 ***
ORIGIN_GRID_ID2773  2.1949123  0.0232821     94.275  < 2e-16 ***
ORIGIN_GRID_ID2798  1.5861885  0.0233787     67.848  < 2e-16 ***
ORIGIN_GRID_ID2799  2.3413552  0.0232642    100.642  < 2e-16 ***
ORIGIN_GRID_ID2800  2.1641159  0.0232865     92.934  < 2e-16 ***
ORIGIN_GRID_ID2824  1.8916401  0.0233825     80.900  < 2e-16 ***
ORIGIN_GRID_ID2825  2.4423714  0.0232589    105.008  < 2e-16 ***
ORIGIN_GRID_ID2826  2.6205062  0.0233068    112.435  < 2e-16 ***
ORIGIN_GRID_ID2827  2.8183816  0.0232755    121.088  < 2e-16 ***
ORIGIN_GRID_ID2852  2.6680986  0.0232891    114.564  < 2e-16 ***
ORIGIN_GRID_ID2853  2.7189345  0.0232537    116.925  < 2e-16 ***
ORIGIN_GRID_ID2854  2.7310983  0.0232610    117.411  < 2e-16 ***
ORIGIN_GRID_ID2878  1.7561640  0.0233723     75.139  < 2e-16 ***
ORIGIN_GRID_ID2879  2.4746224  0.0232847    106.277  < 2e-16 ***
ORIGIN_GRID_ID2880  2.3251736  0.0232855     99.855  < 2e-16 ***
ORIGIN_GRID_ID2881  2.7750839  0.0232690    119.261  < 2e-16 ***
ORIGIN_GRID_ID2907  2.3817211  0.0233176    102.143  < 2e-16 ***
ORIGIN_GRID_ID2908  2.7447405  0.0232830    117.886  < 2e-16 ***
ORIGIN_GRID_ID2933  0.5701004  0.0245064     23.263  < 2e-16 ***
ORIGIN_GRID_ID2934  2.0163148  0.0233339     86.411  < 2e-16 ***
ORIGIN_GRID_ID3098  1.9928416  0.0238055     83.714  < 2e-16 ***
DESTIN_GRID_ID718   0.0823635  0.0044988     18.308  < 2e-16 ***
DESTIN_GRID_ID745  -1.9939132  0.0051018   -390.826  < 2e-16 ***
DESTIN_GRID_ID746  -0.9470953  0.0046995   -201.529  < 2e-16 ***
DESTIN_GRID_ID772  -0.1714047  0.0043693    -39.230  < 2e-16 ***
DESTIN_GRID_ID799   0.2103176  0.0044425     47.343  < 2e-16 ***
DESTIN_GRID_ID800  -1.0145039  0.0044925   -225.823  < 2e-16 ***
DESTIN_GRID_ID826   1.4296727  0.0043520    328.510  < 2e-16 ***
DESTIN_GRID_ID827  -0.0261523  0.0045821     -5.707 1.15e-08 ***
DESTIN_GRID_ID854  -1.3074540  0.0048204   -271.233  < 2e-16 ***
DESTIN_GRID_ID880  -1.7866769  0.0054340   -328.795  < 2e-16 ***
DESTIN_GRID_ID881  -1.1496039  0.0054470   -211.052  < 2e-16 ***
DESTIN_GRID_ID908  -0.7412035  0.0046001   -161.128  < 2e-16 ***
DESTIN_GRID_ID934  -0.5367163  0.0046128   -116.354  < 2e-16 ***
DESTIN_GRID_ID935  -0.7987989  0.0046979   -170.032  < 2e-16 ***
DESTIN_GRID_ID961  -0.9511110  0.0048298   -196.928  < 2e-16 ***
DESTIN_GRID_ID962   1.3906919  0.0044201    314.630  < 2e-16 ***
DESTIN_GRID_ID987   0.3625368  0.0045130     80.332  < 2e-16 ***
DESTIN_GRID_ID988  -1.9095357  0.0053643   -355.971  < 2e-16 ***
DESTIN_GRID_ID989  -0.5775397  0.0046354   -124.592  < 2e-16 ***
DESTIN_GRID_ID1015 -3.3568406  0.0094606   -354.825  < 2e-16 ***
DESTIN_GRID_ID1016 -1.5490237  0.0049184   -314.946  < 2e-16 ***
DESTIN_GRID_ID1043 -0.6893444  0.0051338   -134.276  < 2e-16 ***
DESTIN_GRID_ID1068 -2.9439457  0.0210822   -139.641  < 2e-16 ***
DESTIN_GRID_ID1070 -0.3003529  0.0045749    -65.652  < 2e-16 ***
DESTIN_GRID_ID1096 -0.8072654  0.0046611   -173.191  < 2e-16 ***
DESTIN_GRID_ID1097 -1.2524697  0.0051443   -243.469  < 2e-16 ***
DESTIN_GRID_ID1099 -1.0558506  0.0047761   -221.071  < 2e-16 ***
DESTIN_GRID_ID1122 -0.0471629  0.0048825     -9.660  < 2e-16 ***
DESTIN_GRID_ID1123  0.9231916  0.0044351    208.156  < 2e-16 ***
DESTIN_GRID_ID1124 -0.4216772  0.0046771    -90.157  < 2e-16 ***
DESTIN_GRID_ID1125 -1.2703994  0.0051340   -247.447  < 2e-16 ***
DESTIN_GRID_ID1127 -1.8894680  0.0048631   -388.531  < 2e-16 ***
DESTIN_GRID_ID1128 -0.7553649  0.0050946   -148.269  < 2e-16 ***
DESTIN_GRID_ID1148 -1.0911877  0.0052601   -207.448  < 2e-16 ***
DESTIN_GRID_ID1150 -0.3469434  0.0046223    -75.059  < 2e-16 ***
DESTIN_GRID_ID1151 -1.1280472  0.0047968   -235.166  < 2e-16 ***
DESTIN_GRID_ID1152 -1.2148721  0.0054577   -222.599  < 2e-16 ***
DESTIN_GRID_ID1153 -1.5837785  0.0048119   -329.136  < 2e-16 ***
DESTIN_GRID_ID1154  0.6972009  0.0045499    153.234  < 2e-16 ***
DESTIN_GRID_ID1155 -4.0144873  0.0177955   -225.590  < 2e-16 ***
DESTIN_GRID_ID1176 -0.1048868  0.0046404    -22.603  < 2e-16 ***
DESTIN_GRID_ID1178 -1.1398480  0.0047441   -240.267  < 2e-16 ***
DESTIN_GRID_ID1179 -2.0660169  0.0053464   -386.429  < 2e-16 ***
DESTIN_GRID_ID1180 -3.5533893  0.0110291   -322.183  < 2e-16 ***
DESTIN_GRID_ID1181 -0.8437415  0.0046293   -182.260  < 2e-16 ***
DESTIN_GRID_ID1182 -1.2955460  0.0049016   -264.311  < 2e-16 ***
DESTIN_GRID_ID1183 -1.1718745  0.0066371   -176.565  < 2e-16 ***
DESTIN_GRID_ID1205  0.7458944  0.0044843    166.335  < 2e-16 ***
DESTIN_GRID_ID1206 -0.7798289  0.0047935   -162.684  < 2e-16 ***
DESTIN_GRID_ID1207 -1.2047369  0.0049191   -244.910  < 2e-16 ***
DESTIN_GRID_ID1209  0.4281271  0.0046534     92.002  < 2e-16 ***
DESTIN_GRID_ID1232 -0.2236771  0.0045893    -48.739  < 2e-16 ***
DESTIN_GRID_ID1233  0.1633005  0.0047703     34.233  < 2e-16 ***
DESTIN_GRID_ID1235 -0.0660369  0.0046843    -14.098  < 2e-16 ***
DESTIN_GRID_ID1255  0.3782840  0.0070255     53.844  < 2e-16 ***
DESTIN_GRID_ID1258  0.6976707  0.0046345    150.537  < 2e-16 ***
DESTIN_GRID_ID1259 -1.0528039  0.0050102   -210.131  < 2e-16 ***
DESTIN_GRID_ID1261 -1.2534776  0.0049092   -255.333  < 2e-16 ***
DESTIN_GRID_ID1262 -0.5183322  0.0047543   -109.024  < 2e-16 ***
DESTIN_GRID_ID1283 -0.8828822  0.0050313   -175.477  < 2e-16 ***
DESTIN_GRID_ID1284 -1.2079761  0.0062578   -193.036  < 2e-16 ***
DESTIN_GRID_ID1286 -1.7567254  0.0061821   -284.162  < 2e-16 ***
DESTIN_GRID_ID1289 -0.1561723  0.0045910    -34.017  < 2e-16 ***
DESTIN_GRID_ID1309  0.7419761  0.0047173    157.288  < 2e-16 ***
DESTIN_GRID_ID1310  1.4503139  0.0044839    323.447  < 2e-16 ***
DESTIN_GRID_ID1315  0.6725445  0.0045369    148.239  < 2e-16 ***
DESTIN_GRID_ID1316 -1.7723623  0.0056715   -312.502  < 2e-16 ***
DESTIN_GRID_ID1337 -0.6735359  0.0047466   -141.898  < 2e-16 ***
DESTIN_GRID_ID1338 -1.2743110  0.0072052   -176.861  < 2e-16 ***
DESTIN_GRID_ID1343 -1.6111474  0.0051761   -311.269  < 2e-16 ***
DESTIN_GRID_ID1363  0.4886895  0.0048672    100.404  < 2e-16 ***
DESTIN_GRID_ID1364 -1.0111984  0.0051830   -195.098  < 2e-16 ***
DESTIN_GRID_ID1366 -0.4122033  0.0050431    -81.736  < 2e-16 ***
DESTIN_GRID_ID1369 -0.4335663  0.0048032    -90.266  < 2e-16 ***
DESTIN_GRID_ID1370 -0.3950713  0.0049284    -80.161  < 2e-16 ***
DESTIN_GRID_ID1374 -1.3224679  0.0054686   -241.830  < 2e-16 ***
DESTIN_GRID_ID1375 -1.2435537  0.0071576   -173.739  < 2e-16 ***
DESTIN_GRID_ID1391 -0.6388905  0.0057982   -110.188  < 2e-16 ***
DESTIN_GRID_ID1392 -1.5897483  0.0077727   -204.530  < 2e-16 ***
DESTIN_GRID_ID1396 -2.1931821  0.0093291   -235.090  < 2e-16 ***
DESTIN_GRID_ID1397 -1.1907254  0.0050600   -235.323  < 2e-16 ***
DESTIN_GRID_ID1401  0.9230199  0.0047719    193.429  < 2e-16 ***
DESTIN_GRID_ID1402 -0.3510245  0.0049049    -71.567  < 2e-16 ***
DESTIN_GRID_ID1423 -0.9092900  0.0060248   -150.923  < 2e-16 ***
DESTIN_GRID_ID1428 -1.0097336  0.0051675   -195.400  < 2e-16 ***
DESTIN_GRID_ID1429 -0.6552511  0.0052869   -123.939  < 2e-16 ***
DESTIN_GRID_ID1455 -0.9336179  0.0052206   -178.835  < 2e-16 ***
DESTIN_GRID_ID1456 -1.2052699  0.0051050   -236.098  < 2e-16 ***
DESTIN_GRID_ID1471  0.0839861  0.0051595     16.278  < 2e-16 ***
DESTIN_GRID_ID1482  0.4415548  0.0047415     93.125  < 2e-16 ***
DESTIN_GRID_ID1499 -0.9453817  0.0063606   -148.630  < 2e-16 ***
DESTIN_GRID_ID1509 -1.4003651  0.0064652   -216.599  < 2e-16 ***
DESTIN_GRID_ID1510  1.5437071  0.0046573    331.460  < 2e-16 ***
DESTIN_GRID_ID1525  0.6879113  0.0046849    146.836  < 2e-16 ***
DESTIN_GRID_ID1536 -0.0849519  0.0047724    -17.801  < 2e-16 ***
DESTIN_GRID_ID1537 -0.5377033  0.0051984   -103.436  < 2e-16 ***
DESTIN_GRID_ID1552 -2.0491819  0.0103726   -197.557  < 2e-16 ***
DESTIN_GRID_ID1553 -0.7478107  0.0053444   -139.925  < 2e-16 ***
DESTIN_GRID_ID1563 -0.0386832  0.0050411     -7.674 1.67e-14 ***
DESTIN_GRID_ID1564 -0.5197407  0.0047717   -108.921  < 2e-16 ***
DESTIN_GRID_ID1578 -1.5154532  0.0076242   -198.768  < 2e-16 ***
DESTIN_GRID_ID1579  0.8466327  0.0047706    177.468  < 2e-16 ***
DESTIN_GRID_ID1590 -0.3791731  0.0048852    -77.616  < 2e-16 ***
DESTIN_GRID_ID1591 -0.2188094  0.0048726    -44.906  < 2e-16 ***
DESTIN_GRID_ID1605  0.1981740  0.0049236     40.250  < 2e-16 ***
DESTIN_GRID_ID1606 -0.0992365  0.0049641    -19.991  < 2e-16 ***
DESTIN_GRID_ID1617 -1.3948054  0.0078930   -176.713  < 2e-16 ***
DESTIN_GRID_ID1618  1.2385581  0.0046698    265.225  < 2e-16 ***
DESTIN_GRID_ID1631 -0.2302454  0.0053202    -43.277  < 2e-16 ***
DESTIN_GRID_ID1632 -0.0930232  0.0050259    -18.509  < 2e-16 ***
DESTIN_GRID_ID1634 -0.0214672  0.0060956     -3.522 0.000429 ***
DESTIN_GRID_ID1644 -0.3319513  0.0050311    -65.980  < 2e-16 ***
DESTIN_GRID_ID1645  0.0200400  0.0048357      4.144 3.41e-05 ***
DESTIN_GRID_ID1658 -0.4441275  0.0054844    -80.979  < 2e-16 ***
DESTIN_GRID_ID1659  0.4429479  0.0047152     93.941  < 2e-16 ***
DESTIN_GRID_ID1672 -0.6446785  0.0056591   -113.919  < 2e-16 ***
DESTIN_GRID_ID1684  0.3408414  0.0049423     68.964  < 2e-16 ***
DESTIN_GRID_ID1685  0.0269252  0.0054829      4.911 9.07e-07 ***
DESTIN_GRID_ID1686  0.0710187  0.0049376     14.383  < 2e-16 ***
DESTIN_GRID_ID1688 -0.6038053  0.0073495    -82.156  < 2e-16 ***
DESTIN_GRID_ID1699 -0.4380429  0.0049069    -89.271  < 2e-16 ***
DESTIN_GRID_ID1700 -0.9087502  0.0074319   -122.277  < 2e-16 ***
DESTIN_GRID_ID1712 -1.1245828  0.0058788   -191.295  < 2e-16 ***
DESTIN_GRID_ID1713  0.8269550  0.0046421    178.143  < 2e-16 ***
DESTIN_GRID_ID1727  0.0256238  0.0048697      5.262 1.43e-07 ***
DESTIN_GRID_ID1739  0.8702778  0.0046081    188.860  < 2e-16 ***
DESTIN_GRID_ID1753  1.0393273  0.0046832    221.926  < 2e-16 ***
DESTIN_GRID_ID1754 -0.6132714  0.0051817   -118.352  < 2e-16 ***
DESTIN_GRID_ID1766  0.3906897  0.0047356     82.501  < 2e-16 ***
DESTIN_GRID_ID1767  0.2590744  0.0046854     55.294  < 2e-16 ***
DESTIN_GRID_ID1780 -0.7437489  0.0109600    -67.860  < 2e-16 ***
DESTIN_GRID_ID1781 -0.6749109  0.0050261   -134.282  < 2e-16 ***
DESTIN_GRID_ID1792 -0.6416914  0.0052725   -121.705  < 2e-16 ***
DESTIN_GRID_ID1793  0.4772098  0.0046617    102.367  < 2e-16 ***
DESTIN_GRID_ID1794 -0.4810283  0.0055449    -86.751  < 2e-16 ***
DESTIN_GRID_ID1807 -1.7807697  0.0055631   -320.101  < 2e-16 ***
DESTIN_GRID_ID1820 -0.2611087  0.0050957    -51.241  < 2e-16 ***
DESTIN_GRID_ID1821  1.4569495  0.0046014    316.633  < 2e-16 ***
DESTIN_GRID_ID1833  0.1888601  0.0047049     40.142  < 2e-16 ***
DESTIN_GRID_ID1835 -1.3866546  0.0057166   -242.567  < 2e-16 ***
DESTIN_GRID_ID1847 -1.6970031  0.0101958   -166.442  < 2e-16 ***
DESTIN_GRID_ID1854 -0.6101389  0.0055786   -109.372  < 2e-16 ***
DESTIN_GRID_ID1859 -1.2346833  0.0048945   -252.259  < 2e-16 ***
DESTIN_GRID_ID1860 -0.9599236  0.0049357   -194.485  < 2e-16 ***
DESTIN_GRID_ID1861 -1.0004004  0.0056169   -178.104  < 2e-16 ***
DESTIN_GRID_ID1874  0.1344488  0.0048960     27.461  < 2e-16 ***
DESTIN_GRID_ID1875  0.3885619  0.0046924     82.806  < 2e-16 ***
DESTIN_GRID_ID1882  0.1719441  0.0047633     36.098  < 2e-16 ***
DESTIN_GRID_ID1883 -1.2151781  0.0057315   -212.019  < 2e-16 ***
DESTIN_GRID_ID1886  1.2617086  0.0046466    271.532  < 2e-16 ***
DESTIN_GRID_ID1887  1.1214607  0.0046425    241.565  < 2e-16 ***
DESTIN_GRID_ID1888 -1.1466732  0.0055977   -204.846  < 2e-16 ***
DESTIN_GRID_ID1905 -0.9464612  0.0058131   -162.816  < 2e-16 ***
DESTIN_GRID_ID1907 -0.0488866  0.0049985     -9.780  < 2e-16 ***
DESTIN_GRID_ID1908 -0.9346275  0.0053995   -173.096  < 2e-16 ***
DESTIN_GRID_ID1909 -0.6272505  0.0049941   -125.598  < 2e-16 ***
DESTIN_GRID_ID1912 -4.1136344  0.0214419   -191.851  < 2e-16 ***
DESTIN_GRID_ID1913 -0.9907943  0.0048719   -203.368  < 2e-16 ***
DESTIN_GRID_ID1914 -0.4058389  0.0047943    -84.650  < 2e-16 ***
DESTIN_GRID_ID1928 -0.0293996  0.0052069     -5.646 1.64e-08 ***
DESTIN_GRID_ID1929  0.0468685  0.0052624      8.906  < 2e-16 ***
DESTIN_GRID_ID1933  0.4083978  0.0047662     85.687  < 2e-16 ***
DESTIN_GRID_ID1935 -0.2038334  0.0049700    -41.013  < 2e-16 ***
DESTIN_GRID_ID1936 -0.6005226  0.0049483   -121.359  < 2e-16 ***
DESTIN_GRID_ID1937 -0.4829339  0.0049779    -97.016  < 2e-16 ***
DESTIN_GRID_ID1940 -1.0582161  0.0049831   -212.361  < 2e-16 ***
DESTIN_GRID_ID1941 -2.2463990  0.0055040   -408.140  < 2e-16 ***
DESTIN_GRID_ID1942 -1.1030514  0.0063609   -173.411  < 2e-16 ***
DESTIN_GRID_ID1955  1.1606670  0.0047155    246.138  < 2e-16 ***
DESTIN_GRID_ID1959  0.3098983  0.0047566     65.151  < 2e-16 ***
DESTIN_GRID_ID1960  0.4870625  0.0046846    103.971  < 2e-16 ***
DESTIN_GRID_ID1962 -0.8760734  0.0050396   -173.839  < 2e-16 ***
DESTIN_GRID_ID1963 -1.0697557  0.0049649   -215.463  < 2e-16 ***
DESTIN_GRID_ID1967 -0.7845006  0.0048893   -160.452  < 2e-16 ***
DESTIN_GRID_ID1968 -0.9202556  0.0050918   -180.735  < 2e-16 ***
DESTIN_GRID_ID1985  0.2486742  0.0050459     49.282  < 2e-16 ***
DESTIN_GRID_ID1987  1.0359625  0.0045892    225.740  < 2e-16 ***
DESTIN_GRID_ID1988 -0.8969305  0.0051196   -175.196  < 2e-16 ***
DESTIN_GRID_ID1989 -1.1466382  0.0053461   -214.481  < 2e-16 ***
DESTIN_GRID_ID1990  1.5164341  0.0045752    331.445  < 2e-16 ***
DESTIN_GRID_ID1994 -3.4364132  0.0132377   -259.593  < 2e-16 ***
DESTIN_GRID_ID1995 -1.5186548  0.0051596   -294.335  < 2e-16 ***
DESTIN_GRID_ID2010  0.6093918  0.0046518    131.002  < 2e-16 ***
DESTIN_GRID_ID2011  0.5794824  0.0047660    121.588  < 2e-16 ***
DESTIN_GRID_ID2012 -0.7308218  0.0054020   -135.288  < 2e-16 ***
DESTIN_GRID_ID2013 -0.6230363  0.0048022   -129.741  < 2e-16 ***
DESTIN_GRID_ID2014 -0.4573344  0.0047669    -95.940  < 2e-16 ***
DESTIN_GRID_ID2015  0.2353482  0.0050299     46.790  < 2e-16 ***
DESTIN_GRID_ID2016 -0.6477758  0.0048718   -132.965  < 2e-16 ***
DESTIN_GRID_ID2017 -0.7050569  0.0048634   -144.972  < 2e-16 ***
DESTIN_GRID_ID2021 -2.9281585  0.0078343   -373.762  < 2e-16 ***
DESTIN_GRID_ID2038  1.1628168  0.0045990    252.839  < 2e-16 ***
DESTIN_GRID_ID2039 -0.4087936  0.0053534    -76.362  < 2e-16 ***
DESTIN_GRID_ID2040 -0.2310502  0.0049394    -46.777  < 2e-16 ***
DESTIN_GRID_ID2041  0.3422292  0.0047177     72.542  < 2e-16 ***
DESTIN_GRID_ID2042 -0.2895773  0.0053426    -54.201  < 2e-16 ***
DESTIN_GRID_ID2043 -0.0906411  0.0049641    -18.259  < 2e-16 ***
DESTIN_GRID_ID2044 -0.4740757  0.0047599    -99.598  < 2e-16 ***
DESTIN_GRID_ID2064  0.3354812  0.0049794     67.373  < 2e-16 ***
DESTIN_GRID_ID2065 -0.0117657  0.0049764     -2.364 0.018063 *  
DESTIN_GRID_ID2066 -0.2189721  0.0047616    -45.987  < 2e-16 ***
DESTIN_GRID_ID2067 -0.8834517  0.0052929   -166.911  < 2e-16 ***
DESTIN_GRID_ID2068 -0.6727622  0.0050582   -133.003  < 2e-16 ***
DESTIN_GRID_ID2070 -0.1796469  0.0050327    -35.696  < 2e-16 ***
DESTIN_GRID_ID2071 -0.1511985  0.0048678    -31.061  < 2e-16 ***
DESTIN_GRID_ID2093  0.3554040  0.0046938     75.718  < 2e-16 ***
DESTIN_GRID_ID2094  0.0161963  0.0047949      3.378 0.000731 ***
DESTIN_GRID_ID2095 -0.4603336  0.0052794    -87.194  < 2e-16 ***
DESTIN_GRID_ID2098 -0.5164101  0.0051374   -100.520  < 2e-16 ***
DESTIN_GRID_ID2119  0.0408520  0.0049664      8.226  < 2e-16 ***
DESTIN_GRID_ID2120  0.6229453  0.0047374    131.496  < 2e-16 ***
DESTIN_GRID_ID2123 -1.2434369  0.0054246   -229.223  < 2e-16 ***
DESTIN_GRID_ID2147  0.2654927  0.0047495     55.898  < 2e-16 ***
DESTIN_GRID_ID2148  0.0986195  0.0047861     20.606  < 2e-16 ***
DESTIN_GRID_ID2149  0.3192016  0.0048721     65.516  < 2e-16 ***
DESTIN_GRID_ID2150 -1.8508006  0.0073523   -251.732  < 2e-16 ***
DESTIN_GRID_ID2151 -2.2085603  0.0067416   -327.602  < 2e-16 ***
DESTIN_GRID_ID2152  0.1218096  0.0047311     25.747  < 2e-16 ***
DESTIN_GRID_ID2154 -2.1746261  0.0063668   -341.558  < 2e-16 ***
DESTIN_GRID_ID2174 -1.5958357  0.0064728   -246.543  < 2e-16 ***
DESTIN_GRID_ID2177  1.7451425  0.0045625    382.499  < 2e-16 ***
DESTIN_GRID_ID2178 -1.6935187  0.0051449   -329.164  < 2e-16 ***
DESTIN_GRID_ID2179 -0.5104683  0.0047885   -106.603  < 2e-16 ***
DESTIN_GRID_ID2180 -1.4204037  0.0056587   -251.014  < 2e-16 ***
DESTIN_GRID_ID2201 -0.0771968  0.0049136    -15.711  < 2e-16 ***
DESTIN_GRID_ID2203 -0.1211412  0.0055884    -21.677  < 2e-16 ***
DESTIN_GRID_ID2204 -0.2062654  0.0049414    -41.742  < 2e-16 ***
DESTIN_GRID_ID2205 -1.1609010  0.0049182   -236.040  < 2e-16 ***
DESTIN_GRID_ID2206 -0.2239748  0.0046764    -47.895  < 2e-16 ***
DESTIN_GRID_ID2208 -1.0669830  0.0050711   -210.404  < 2e-16 ***
DESTIN_GRID_ID2228 -0.4848175  0.0050602    -95.811  < 2e-16 ***
DESTIN_GRID_ID2231 -0.6842577  0.0048987   -139.683  < 2e-16 ***
DESTIN_GRID_ID2233 -0.3601573  0.0046626    -77.245  < 2e-16 ***
DESTIN_GRID_ID2234 -6.7699994  0.0914050    -74.066  < 2e-16 ***
DESTIN_GRID_ID2235 -3.6543254  0.0316189   -115.574  < 2e-16 ***
DESTIN_GRID_ID2254 -0.2630740  0.0072550    -36.261  < 2e-16 ***
DESTIN_GRID_ID2255 -0.6986636  0.0059086   -118.246  < 2e-16 ***
DESTIN_GRID_ID2256 -0.3150151  0.0050148    -62.817  < 2e-16 ***
DESTIN_GRID_ID2257 -0.7764905  0.0088414    -87.824  < 2e-16 ***
DESTIN_GRID_ID2259 -1.4601599  0.0061323   -238.110  < 2e-16 ***
DESTIN_GRID_ID2260 -1.3031982  0.0048693   -267.636  < 2e-16 ***
DESTIN_GRID_ID2261 -1.1573761  0.0048699   -237.657  < 2e-16 ***
DESTIN_GRID_ID2262 -2.3272902  0.0065242   -356.717  < 2e-16 ***
DESTIN_GRID_ID2281 -0.5246140  0.0058733    -89.322  < 2e-16 ***
DESTIN_GRID_ID2282  0.7694415  0.0047143    163.213  < 2e-16 ***
DESTIN_GRID_ID2283 -0.4499669  0.0050680    -88.786  < 2e-16 ***
DESTIN_GRID_ID2285 -0.0605570  0.0048461    -12.496  < 2e-16 ***
DESTIN_GRID_ID2286 -1.0925783  0.0051112   -213.760  < 2e-16 ***
DESTIN_GRID_ID2287 -0.3405048  0.0046237    -73.643  < 2e-16 ***
DESTIN_GRID_ID2288 -2.8580538  0.0080824   -353.615  < 2e-16 ***
DESTIN_GRID_ID2310 -0.0149109  0.0048306     -3.087 0.002023 ** 
DESTIN_GRID_ID2312 -1.4071916  0.0066516   -211.558  < 2e-16 ***
DESTIN_GRID_ID2313  0.5898960  0.0046241    127.570  < 2e-16 ***
DESTIN_GRID_ID2314  0.5984642  0.0045728    130.876  < 2e-16 ***
DESTIN_GRID_ID2315 -1.4029063  0.0050501   -277.797  < 2e-16 ***
DESTIN_GRID_ID2316 -0.7437539  0.0047657   -156.065  < 2e-16 ***
DESTIN_GRID_ID2335 -1.8037341  0.0142388   -126.677  < 2e-16 ***
DESTIN_GRID_ID2339 -0.3409666  0.0050155    -67.983  < 2e-16 ***
DESTIN_GRID_ID2340 -0.6530266  0.0047143   -138.521  < 2e-16 ***
DESTIN_GRID_ID2341 -0.4762468  0.0046427   -102.580  < 2e-16 ***
DESTIN_GRID_ID2342 -1.7669356  0.0049396   -357.707  < 2e-16 ***
DESTIN_GRID_ID2343 -1.9749135  0.0057755   -341.949  < 2e-16 ***
DESTIN_GRID_ID2363 -0.8245232  0.0057808   -142.632  < 2e-16 ***
DESTIN_GRID_ID2367 -0.6724198  0.0053520   -125.640  < 2e-16 ***
DESTIN_GRID_ID2368 -0.9142324  0.0048653   -187.909  < 2e-16 ***
DESTIN_GRID_ID2369 -0.0873500  0.0046743    -18.687  < 2e-16 ***
DESTIN_GRID_ID2370  0.6712261  0.0045889    146.272  < 2e-16 ***
DESTIN_GRID_ID2371 -1.1654716  0.0050836   -229.263  < 2e-16 ***
DESTIN_GRID_ID2390  0.7529140  0.0047061    159.987  < 2e-16 ***
DESTIN_GRID_ID2391  0.3709119  0.0047854     77.509  < 2e-16 ***
DESTIN_GRID_ID2394 -2.2788310  0.0073299   -310.894  < 2e-16 ***
DESTIN_GRID_ID2395 -0.8492635  0.0048119   -176.491  < 2e-16 ***
DESTIN_GRID_ID2396 -0.9481859  0.0047091   -201.353  < 2e-16 ***
DESTIN_GRID_ID2397 -2.5417252  0.0070567   -360.187  < 2e-16 ***
DESTIN_GRID_ID2398 -1.7913026  0.0058240   -307.575  < 2e-16 ***
DESTIN_GRID_ID2418 -0.2195260  0.0051601    -42.543  < 2e-16 ***
DESTIN_GRID_ID2419  0.3976763  0.0049105     80.985  < 2e-16 ***
DESTIN_GRID_ID2422 -1.9538068  0.0100967   -193.509  < 2e-16 ***
DESTIN_GRID_ID2423 -1.9402225  0.0055339   -350.605  < 2e-16 ***
DESTIN_GRID_ID2424 -0.5548246  0.0047029   -117.976  < 2e-16 ***
DESTIN_GRID_ID2425  0.7485421  0.0046374    161.414  < 2e-16 ***
DESTIN_GRID_ID2426 -0.9674374  0.0062861   -153.901  < 2e-16 ***
DESTIN_GRID_ID2443  0.8071604  0.0047640    169.429  < 2e-16 ***
DESTIN_GRID_ID2445  0.2263214  0.0047915     47.234  < 2e-16 ***
DESTIN_GRID_ID2449 -2.0577031  0.0074837   -274.957  < 2e-16 ***
DESTIN_GRID_ID2450 -1.6773878  0.0050996   -328.926  < 2e-16 ***
DESTIN_GRID_ID2451 -0.2573648  0.0046617    -55.208  < 2e-16 ***
DESTIN_GRID_ID2472 -2.2801445  0.0167678   -135.984  < 2e-16 ***
DESTIN_GRID_ID2473  0.2335433  0.0049313     47.360  < 2e-16 ***
DESTIN_GRID_ID2478 -1.5072930  0.0051208   -294.348  < 2e-16 ***
DESTIN_GRID_ID2479 -2.3028657  0.0088907   -259.020  < 2e-16 ***
DESTIN_GRID_ID2497 -0.2663018  0.0050397    -52.841  < 2e-16 ***
DESTIN_GRID_ID2499 -0.8890810  0.0058019   -153.240  < 2e-16 ***
DESTIN_GRID_ID2505 -1.3480014  0.0053153   -253.609  < 2e-16 ***
DESTIN_GRID_ID2527  0.6177898  0.0047186    130.926  < 2e-16 ***
DESTIN_GRID_ID2532 -1.9998102  0.0061208   -326.726  < 2e-16 ***
DESTIN_GRID_ID2533 -1.7952434  0.0078494   -228.712  < 2e-16 ***
DESTIN_GRID_ID2551 -0.2278808  0.0056551    -40.297  < 2e-16 ***
DESTIN_GRID_ID2553 -1.2030442  0.0071382   -168.537  < 2e-16 ***
DESTIN_GRID_ID2554 -1.8046064  0.0083553   -215.984  < 2e-16 ***
DESTIN_GRID_ID2559 -1.9163594  0.0072285   -265.110  < 2e-16 ***
DESTIN_GRID_ID2580 -0.2781583  0.0049352    -56.362  < 2e-16 ***
DESTIN_GRID_ID2581 -1.1813498  0.0066405   -177.899  < 2e-16 ***
DESTIN_GRID_ID2607 -0.7061521  0.0050071   -141.031  < 2e-16 ***
DESTIN_GRID_ID2608 -1.3336677  0.0069616   -191.575  < 2e-16 ***
DESTIN_GRID_ID2634  1.5823460  0.0046138    342.957  < 2e-16 ***
DESTIN_GRID_ID2635 -1.1151794  0.0056520   -197.307  < 2e-16 ***
DESTIN_GRID_ID2636 -0.0436951  0.0049959     -8.746  < 2e-16 ***
DESTIN_GRID_ID2661 -0.8105257  0.0049149   -164.912  < 2e-16 ***
DESTIN_GRID_ID2663  0.1243880  0.0047374     26.257  < 2e-16 ***
DESTIN_GRID_ID2665  0.1299624  0.0048231     26.946  < 2e-16 ***
DESTIN_GRID_ID2688 -0.6012795  0.0050566   -118.911  < 2e-16 ***
DESTIN_GRID_ID2689  0.3445226  0.0047568     72.428  < 2e-16 ***
DESTIN_GRID_ID2690 -0.1938592  0.0048178    -40.238  < 2e-16 ***
DESTIN_GRID_ID2691 -0.4264559  0.0048296    -88.300  < 2e-16 ***
DESTIN_GRID_ID2693 -0.1808260  0.0049380    -36.619  < 2e-16 ***
DESTIN_GRID_ID2715 -0.5474280  0.0052156   -104.960  < 2e-16 ***
DESTIN_GRID_ID2717 -0.4753838  0.0047398   -100.297  < 2e-16 ***
DESTIN_GRID_ID2718 -1.4866806  0.0058596   -253.715  < 2e-16 ***
DESTIN_GRID_ID2719 -0.3724660  0.0048040    -77.532  < 2e-16 ***
DESTIN_GRID_ID2742 -0.3570821  0.0050022    -71.385  < 2e-16 ***
DESTIN_GRID_ID2743 -0.2297445  0.0056964    -40.332  < 2e-16 ***
DESTIN_GRID_ID2744  0.3605674  0.0047270     76.279  < 2e-16 ***
DESTIN_GRID_ID2745 -0.0003896  0.0047420     -0.082 0.934522    
DESTIN_GRID_ID2747 -1.1899152  0.0053881   -220.843  < 2e-16 ***
DESTIN_GRID_ID2768 -0.2610821  0.0050744    -51.451  < 2e-16 ***
DESTIN_GRID_ID2771  1.7626264  0.0046023    382.986  < 2e-16 ***
DESTIN_GRID_ID2773 -1.2440055  0.0051455   -241.765  < 2e-16 ***
DESTIN_GRID_ID2798 -1.4982628  0.0061944   -241.875  < 2e-16 ***
DESTIN_GRID_ID2799 -0.6565652  0.0049232   -133.362  < 2e-16 ***
DESTIN_GRID_ID2800  0.7058575  0.0046579    151.539  < 2e-16 ***
DESTIN_GRID_ID2824  0.8384298  0.0048098    174.318  < 2e-16 ***
DESTIN_GRID_ID2825 -0.2975293  0.0047697    -62.379  < 2e-16 ***
DESTIN_GRID_ID2826 -0.8060536  0.0054871   -146.901  < 2e-16 ***
DESTIN_GRID_ID2827  1.4026959  0.0046411    302.232  < 2e-16 ***
DESTIN_GRID_ID2852 -0.5495604  0.0054603   -100.647  < 2e-16 ***
DESTIN_GRID_ID2853  0.7627822  0.0046340    164.606  < 2e-16 ***
DESTIN_GRID_ID2854 -0.0839692  0.0048168    -17.433  < 2e-16 ***
DESTIN_GRID_ID2878 -0.5407361  0.0054175    -99.812  < 2e-16 ***
DESTIN_GRID_ID2879 -0.4304661  0.0049977    -86.133  < 2e-16 ***
DESTIN_GRID_ID2880 -1.1546351  0.0053480   -215.902  < 2e-16 ***
DESTIN_GRID_ID2881 -0.6354625  0.0051517   -123.351  < 2e-16 ***
DESTIN_GRID_ID2907 -1.1489801  0.0060094   -191.196  < 2e-16 ***
DESTIN_GRID_ID2908 -0.0723882  0.0048592    -14.897  < 2e-16 ***
DESTIN_GRID_ID2933  0.9100037  0.0051342    177.242  < 2e-16 ***
DESTIN_GRID_ID2934 -0.7678002  0.0052786   -145.456  < 2e-16 ***
DESTIN_GRID_ID3098  0.4194702  0.0054598     76.829  < 2e-16 ***
log(DISTANCE)      -1.5303317  0.0001407 -10875.273  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 535353461  on 101714  degrees of freedom
Residual deviance:  96048379  on 101019  degrees of freedom
AIC: 96807997

Number of Fisher Scoring iterations: 6
CalcRSquared(dbcSIM_Poisson$data$TRIPS, dbcSIM_Poisson$fitted.values)
[1] 0.791819

8 Comparing Models

model_list <- list(originConstrained=orcSIM_Poisson,
                   destinationConstrained=decSIM_Poisson,
                   doublyConstrained=dbcSIM_Poisson)
compare_performance(model_list,
                    metrics = "RMSE")
# Comparison of Model Performance Indices

Name                   | Model |     RMSE
-----------------------------------------
originConstrained      |   glm | 3162.491
destinationConstrained |   glm | 3334.765
doublyConstrained      |   glm | 2365.462
df <- as.data.frame(orcSIM_Poisson$fitted.values) %>%
  round(digits = 0)
inter_zonal_flow <- inter_zonal_flow %>%
  cbind(df) %>%
  rename(orcTRIPS = "orcSIM_Poisson$fitted.values")
df2 <- as.data.frame(decSIM_Poisson$fitted.values) %>%
  round(digits = 0)
inter_zonal_flow <- inter_zonal_flow %>%
  cbind(df2) %>%
  rename(decTRIPS = "decSIM_Poisson$fitted.values")
df3 <- as.data.frame(dbcSIM_Poisson$fitted.values) %>%
  round(digits = 0)
inter_zonal_flow <- inter_zonal_flow %>%
  cbind(df3) %>%
  rename(dbcTRIPS = "dbcSIM_Poisson$fitted.values")
orc_p <- ggplot(data = inter_zonal_flow,
                aes(x = orcTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,70000),
                  ylim=c(0,70000))

dec_p <- ggplot(data = inter_zonal_flow,
                aes(x = decTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,70000),
                  ylim=c(0,70000))

dbc_p <- ggplot(data = inter_zonal_flow,
                aes(x = dbcTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,70000),
                  ylim=c(0,70000))
ggarrange(orc_p, dec_p,
          dbc_p,
          ncol = 2,
          nrow = 2)

8.1 Further Calibration of the Models

8.1.1 Remove certain variables

orcSIM_Poisson2 <- glm(formula = TRIPS ~ 
                ORIGIN_GRID_ID +
                log(TDESTIN_BIZ_COUNT) +
                log(TDESTIN_FINSERV_COUNT) +
                  log(TDESTIN_MRTEXIT_COUNT) +
                  log(TDESTIN_BUSSTOP_COUNT) +
                  log(TDESTIN_HDBCOMM_UNITS) +
                  log(TDESTIN_HDBRES_UNITS) + 
                  log(TDESTIN_SCHOOLS_COUNT) + 
                log(DISTANCE) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
summary(orcSIM_Poisson2)

Call:
glm(formula = TRIPS ~ ORIGIN_GRID_ID + log(TDESTIN_BIZ_COUNT) + 
    log(TDESTIN_FINSERV_COUNT) + log(TDESTIN_MRTEXIT_COUNT) + 
    log(TDESTIN_BUSSTOP_COUNT) + log(TDESTIN_HDBCOMM_UNITS) + 
    log(TDESTIN_HDBRES_UNITS) + log(TDESTIN_SCHOOLS_COUNT) + 
    log(DISTANCE) - 1, family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                             Estimate Std. Error   z value Pr(>|z|)    
ORIGIN_GRID_ID664           1.472e+01  2.324e-02    633.61   <2e-16 ***
ORIGIN_GRID_ID718           1.870e+01  1.667e-03  11219.33   <2e-16 ***
ORIGIN_GRID_ID745           1.640e+01  2.759e-03   5944.72   <2e-16 ***
ORIGIN_GRID_ID746           1.843e+01  1.724e-03  10686.52   <2e-16 ***
ORIGIN_GRID_ID772           1.809e+01  1.572e-03  11502.21   <2e-16 ***
ORIGIN_GRID_ID799           1.746e+01  2.442e-03   7150.90   <2e-16 ***
ORIGIN_GRID_ID800           1.861e+01  1.570e-03  11857.18   <2e-16 ***
ORIGIN_GRID_ID826           1.837e+01  1.570e-03  11695.12   <2e-16 ***
ORIGIN_GRID_ID827           1.837e+01  1.813e-03  10133.64   <2e-16 ***
ORIGIN_GRID_ID854           1.721e+01  2.259e-03   7618.77   <2e-16 ***
ORIGIN_GRID_ID880           1.661e+01  2.926e-03   5677.27   <2e-16 ***
ORIGIN_GRID_ID881           1.592e+01  6.075e-03   2619.64   <2e-16 ***
ORIGIN_GRID_ID908           1.813e+01  1.639e-03  11061.73   <2e-16 ***
ORIGIN_GRID_ID934           1.681e+01  2.385e-03   7049.05   <2e-16 ***
ORIGIN_GRID_ID935           1.757e+01  1.864e-03   9422.69   <2e-16 ***
ORIGIN_GRID_ID961           1.794e+01  1.851e-03   9692.50   <2e-16 ***
ORIGIN_GRID_ID962           1.818e+01  1.661e-03  10941.40   <2e-16 ***
ORIGIN_GRID_ID987           1.848e+01  1.659e-03  11144.12   <2e-16 ***
ORIGIN_GRID_ID988           1.695e+01  2.429e-03   6980.29   <2e-16 ***
ORIGIN_GRID_ID989           1.809e+01  1.629e-03  11107.39   <2e-16 ***
ORIGIN_GRID_ID1015          1.691e+01  3.046e-03   5551.10   <2e-16 ***
ORIGIN_GRID_ID1016          1.709e+01  2.031e-03   8413.17   <2e-16 ***
ORIGIN_GRID_ID1043          1.733e+01  2.804e-03   6179.67   <2e-16 ***
ORIGIN_GRID_ID1068          1.495e+01  1.914e-02    781.13   <2e-16 ***
ORIGIN_GRID_ID1070          1.757e+01  1.859e-03   9452.03   <2e-16 ***
ORIGIN_GRID_ID1096          1.710e+01  1.911e-03   8950.06   <2e-16 ***
ORIGIN_GRID_ID1097          1.692e+01  2.629e-03   6436.78   <2e-16 ***
ORIGIN_GRID_ID1099          1.840e+01  1.658e-03  11101.46   <2e-16 ***
ORIGIN_GRID_ID1122          1.806e+01  1.721e-03  10493.86   <2e-16 ***
ORIGIN_GRID_ID1123          1.775e+01  1.743e-03  10188.60   <2e-16 ***
ORIGIN_GRID_ID1124          1.712e+01  2.190e-03   7816.94   <2e-16 ***
ORIGIN_GRID_ID1125          1.771e+01  2.046e-03   8655.19   <2e-16 ***
ORIGIN_GRID_ID1127          1.765e+01  1.699e-03  10388.83   <2e-16 ***
ORIGIN_GRID_ID1128          1.753e+01  2.066e-03   8481.06   <2e-16 ***
ORIGIN_GRID_ID1148          1.662e+01  2.882e-03   5768.22   <2e-16 ***
ORIGIN_GRID_ID1150          1.801e+01  1.570e-03  11467.67   <2e-16 ***
ORIGIN_GRID_ID1151          1.744e+01  1.901e-03   9174.61   <2e-16 ***
ORIGIN_GRID_ID1152          1.763e+01  2.265e-03   7782.96   <2e-16 ***
ORIGIN_GRID_ID1153          1.812e+01  1.776e-03  10198.61   <2e-16 ***
ORIGIN_GRID_ID1154          1.819e+01  1.741e-03  10446.99   <2e-16 ***
ORIGIN_GRID_ID1155          1.491e+01  1.039e-02   1435.28   <2e-16 ***
ORIGIN_GRID_ID1176          1.687e+01  2.455e-03   6872.65   <2e-16 ***
ORIGIN_GRID_ID1178          1.703e+01  1.989e-03   8561.44   <2e-16 ***
ORIGIN_GRID_ID1179          1.674e+01  2.359e-03   7096.20   <2e-16 ***
ORIGIN_GRID_ID1180          1.576e+01  5.509e-03   2860.47   <2e-16 ***
ORIGIN_GRID_ID1181          1.686e+01  1.882e-03   8959.59   <2e-16 ***
ORIGIN_GRID_ID1182          1.774e+01  1.698e-03  10442.91   <2e-16 ***
ORIGIN_GRID_ID1183          1.838e+01  2.362e-03   7780.97   <2e-16 ***
ORIGIN_GRID_ID1205          1.796e+01  1.641e-03  10941.57   <2e-16 ***
ORIGIN_GRID_ID1206          1.709e+01  2.165e-03   7895.19   <2e-16 ***
ORIGIN_GRID_ID1207          1.686e+01  2.735e-03   6166.00   <2e-16 ***
ORIGIN_GRID_ID1209          1.730e+01  2.091e-03   8275.36   <2e-16 ***
ORIGIN_GRID_ID1232          1.772e+01  1.734e-03  10217.99   <2e-16 ***
ORIGIN_GRID_ID1233          1.714e+01  2.834e-03   6048.38   <2e-16 ***
ORIGIN_GRID_ID1235          1.763e+01  2.056e-03   8577.08   <2e-16 ***
ORIGIN_GRID_ID1255          1.624e+01  1.065e-02   1524.99   <2e-16 ***
ORIGIN_GRID_ID1258          1.700e+01  2.987e-03   5690.25   <2e-16 ***
ORIGIN_GRID_ID1259          1.724e+01  2.048e-03   8416.77   <2e-16 ***
ORIGIN_GRID_ID1261          1.683e+01  2.158e-03   7799.14   <2e-16 ***
ORIGIN_GRID_ID1262          1.775e+01  1.798e-03   9873.78   <2e-16 ***
ORIGIN_GRID_ID1283          1.668e+01  2.686e-03   6207.48   <2e-16 ***
ORIGIN_GRID_ID1284          1.723e+01  2.809e-03   6135.57   <2e-16 ***
ORIGIN_GRID_ID1286          1.663e+01  3.777e-03   4404.64   <2e-16 ***
ORIGIN_GRID_ID1289          1.701e+01  1.960e-03   8680.89   <2e-16 ***
ORIGIN_GRID_ID1309          1.825e+01  1.864e-03   9790.88   <2e-16 ***
ORIGIN_GRID_ID1310          1.797e+01  1.682e-03  10685.52   <2e-16 ***
ORIGIN_GRID_ID1315          1.733e+01  1.844e-03   9397.60   <2e-16 ***
ORIGIN_GRID_ID1316          1.619e+01  3.242e-03   4992.45   <2e-16 ***
ORIGIN_GRID_ID1337          1.755e+01  1.779e-03   9865.60   <2e-16 ***
ORIGIN_GRID_ID1338          1.713e+01  5.235e-03   3271.12   <2e-16 ***
ORIGIN_GRID_ID1343          1.672e+01  2.214e-03   7553.03   <2e-16 ***
ORIGIN_GRID_ID1363          1.683e+01  3.259e-03   5164.23   <2e-16 ***
ORIGIN_GRID_ID1364          1.676e+01  2.390e-03   7012.94   <2e-16 ***
ORIGIN_GRID_ID1366          1.702e+01  2.843e-03   5987.24   <2e-16 ***
ORIGIN_GRID_ID1369          1.748e+01  1.746e-03  10009.38   <2e-16 ***
ORIGIN_GRID_ID1370          1.777e+01  1.920e-03   9256.50   <2e-16 ***
ORIGIN_GRID_ID1374          1.657e+01  2.927e-03   5662.21   <2e-16 ***
ORIGIN_GRID_ID1375          1.784e+01  3.312e-03   5386.94   <2e-16 ***
ORIGIN_GRID_ID1391          1.583e+01  4.836e-03   3274.20   <2e-16 ***
ORIGIN_GRID_ID1392          1.614e+01  3.918e-03   4118.76   <2e-16 ***
ORIGIN_GRID_ID1396          1.611e+01  5.987e-03   2690.54   <2e-16 ***
ORIGIN_GRID_ID1397          1.652e+01  2.883e-03   5728.23   <2e-16 ***
ORIGIN_GRID_ID1401          1.762e+01  2.061e-03   8546.12   <2e-16 ***
ORIGIN_GRID_ID1402          1.821e+01  1.679e-03  10850.38   <2e-16 ***
ORIGIN_GRID_ID1423          1.846e+01  5.963e-03   3095.89   <2e-16 ***
ORIGIN_GRID_ID1428          1.774e+01  1.993e-03   8902.07   <2e-16 ***
ORIGIN_GRID_ID1429          1.724e+01  3.217e-03   5360.75   <2e-16 ***
ORIGIN_GRID_ID1455          1.659e+01  2.744e-03   6044.71   <2e-16 ***
ORIGIN_GRID_ID1456          1.783e+01  1.776e-03  10041.34   <2e-16 ***
ORIGIN_GRID_ID1471          1.727e+01  2.131e-03   8105.93   <2e-16 ***
ORIGIN_GRID_ID1482          1.740e+01  1.927e-03   9032.03   <2e-16 ***
ORIGIN_GRID_ID1499          1.727e+01  2.105e-03   8208.35   <2e-16 ***
ORIGIN_GRID_ID1509          1.677e+01  3.495e-03   4797.07   <2e-16 ***
ORIGIN_GRID_ID1510          1.842e+01  1.571e-03  11724.65   <2e-16 ***
ORIGIN_GRID_ID1525          1.677e+01  2.228e-03   7526.65   <2e-16 ***
ORIGIN_GRID_ID1536          1.724e+01  1.838e-03   9383.21   <2e-16 ***
ORIGIN_GRID_ID1537          1.687e+01  3.660e-03   4608.62   <2e-16 ***
ORIGIN_GRID_ID1552          1.357e+01  1.426e-02    951.21   <2e-16 ***
ORIGIN_GRID_ID1553          1.601e+01  2.981e-03   5369.67   <2e-16 ***
ORIGIN_GRID_ID1563          1.689e+01  3.250e-03   5198.06   <2e-16 ***
ORIGIN_GRID_ID1564          1.833e+01  1.555e-03  11788.08   <2e-16 ***
ORIGIN_GRID_ID1578          1.497e+01  7.182e-03   2084.88   <2e-16 ***
ORIGIN_GRID_ID1579          1.728e+01  2.113e-03   8179.53   <2e-16 ***
ORIGIN_GRID_ID1590          1.804e+01  1.637e-03  11021.40   <2e-16 ***
ORIGIN_GRID_ID1591          1.837e+01  1.704e-03  10781.28   <2e-16 ***
ORIGIN_GRID_ID1605          1.630e+01  2.807e-03   5808.03   <2e-16 ***
ORIGIN_GRID_ID1606          1.629e+01  2.771e-03   5879.46   <2e-16 ***
ORIGIN_GRID_ID1617          1.629e+01  5.781e-03   2817.52   <2e-16 ***
ORIGIN_GRID_ID1618          1.805e+01  1.742e-03  10362.01   <2e-16 ***
ORIGIN_GRID_ID1631          1.545e+01  5.167e-03   2990.12   <2e-16 ***
ORIGIN_GRID_ID1632          1.688e+01  2.192e-03   7698.86   <2e-16 ***
ORIGIN_GRID_ID1634          1.668e+01  3.715e-03   4490.24   <2e-16 ***
ORIGIN_GRID_ID1644          1.691e+01  2.592e-03   6524.86   <2e-16 ***
ORIGIN_GRID_ID1645          1.814e+01  1.742e-03  10410.86   <2e-16 ***
ORIGIN_GRID_ID1658          1.743e+01  2.279e-03   7647.52   <2e-16 ***
ORIGIN_GRID_ID1659          1.677e+01  2.192e-03   7646.86   <2e-16 ***
ORIGIN_GRID_ID1672          1.696e+01  3.381e-03   5015.09   <2e-16 ***
ORIGIN_GRID_ID1684          1.696e+01  2.531e-03   6698.22   <2e-16 ***
ORIGIN_GRID_ID1685          1.613e+01  3.544e-03   4551.99   <2e-16 ***
ORIGIN_GRID_ID1686          1.667e+01  2.335e-03   7139.68   <2e-16 ***
ORIGIN_GRID_ID1688          1.428e+01  1.649e-02    865.52   <2e-16 ***
ORIGIN_GRID_ID1699          1.639e+01  2.660e-03   6161.38   <2e-16 ***
ORIGIN_GRID_ID1700          1.421e+01  2.247e-02    632.41   <2e-16 ***
ORIGIN_GRID_ID1712          1.612e+01  3.564e-03   4523.20   <2e-16 ***
ORIGIN_GRID_ID1713          1.739e+01  1.773e-03   9806.67   <2e-16 ***
ORIGIN_GRID_ID1727          1.839e+01  1.553e-03  11840.56   <2e-16 ***
ORIGIN_GRID_ID1739          1.661e+01  2.219e-03   7484.20   <2e-16 ***
ORIGIN_GRID_ID1753          1.804e+01  1.696e-03  10636.44   <2e-16 ***
ORIGIN_GRID_ID1754          1.730e+01  2.647e-03   6536.42   <2e-16 ***
ORIGIN_GRID_ID1766          1.769e+01  1.739e-03  10173.33   <2e-16 ***
ORIGIN_GRID_ID1767          1.702e+01  1.771e-03   9610.38   <2e-16 ***
ORIGIN_GRID_ID1780          1.540e+01  5.805e-03   2652.25   <2e-16 ***
ORIGIN_GRID_ID1781          1.724e+01  1.857e-03   9285.51   <2e-16 ***
ORIGIN_GRID_ID1792          1.660e+01  2.541e-03   6535.02   <2e-16 ***
ORIGIN_GRID_ID1793          1.725e+01  1.736e-03   9939.14   <2e-16 ***
ORIGIN_GRID_ID1794          1.577e+01  3.638e-03   4333.39   <2e-16 ***
ORIGIN_GRID_ID1807          1.681e+01  2.129e-03   7895.71   <2e-16 ***
ORIGIN_GRID_ID1820          1.652e+01  2.637e-03   6263.25   <2e-16 ***
ORIGIN_GRID_ID1821          1.780e+01  1.628e-03  10929.60   <2e-16 ***
ORIGIN_GRID_ID1833          1.768e+01  1.620e-03  10910.83   <2e-16 ***
ORIGIN_GRID_ID1835          1.727e+01  2.416e-03   7145.26   <2e-16 ***
ORIGIN_GRID_ID1847          1.680e+01  3.840e-03   4374.83   <2e-16 ***
ORIGIN_GRID_ID1854          1.582e+01  5.680e-03   2784.30   <2e-16 ***
ORIGIN_GRID_ID1859          1.665e+01  1.901e-03   8757.89   <2e-16 ***
ORIGIN_GRID_ID1860          1.711e+01  1.814e-03   9428.07   <2e-16 ***
ORIGIN_GRID_ID1861          1.781e+01  2.003e-03   8894.79   <2e-16 ***
ORIGIN_GRID_ID1874          1.623e+01  2.893e-03   5611.38   <2e-16 ***
ORIGIN_GRID_ID1875          1.660e+01  2.032e-03   8168.29   <2e-16 ***
ORIGIN_GRID_ID1882          1.717e+01  2.043e-03   8406.66   <2e-16 ***
ORIGIN_GRID_ID1883          1.658e+01  3.325e-03   4986.10   <2e-16 ***
ORIGIN_GRID_ID1886          1.787e+01  1.720e-03  10385.71   <2e-16 ***
ORIGIN_GRID_ID1887          1.770e+01  1.658e-03  10680.06   <2e-16 ***
ORIGIN_GRID_ID1888          1.689e+01  2.609e-03   6474.37   <2e-16 ***
ORIGIN_GRID_ID1905          1.513e+01  4.631e-03   3266.64   <2e-16 ***
ORIGIN_GRID_ID1907          1.667e+01  2.675e-03   6231.18   <2e-16 ***
ORIGIN_GRID_ID1908          1.600e+01  3.485e-03   4591.57   <2e-16 ***
ORIGIN_GRID_ID1909          1.724e+01  1.856e-03   9288.34   <2e-16 ***
ORIGIN_GRID_ID1912          1.524e+01  8.549e-03   1782.82   <2e-16 ***
ORIGIN_GRID_ID1913          1.655e+01  2.256e-03   7338.11   <2e-16 ***
ORIGIN_GRID_ID1914          1.819e+01  1.612e-03  11289.00   <2e-16 ***
ORIGIN_GRID_ID1928          1.541e+01  2.985e-03   5162.28   <2e-16 ***
ORIGIN_GRID_ID1929          1.530e+01  4.123e-03   3710.70   <2e-16 ***
ORIGIN_GRID_ID1933          1.628e+01  2.966e-03   5487.87   <2e-16 ***
ORIGIN_GRID_ID1935          1.675e+01  2.582e-03   6489.29   <2e-16 ***
ORIGIN_GRID_ID1936          1.709e+01  2.079e-03   8219.99   <2e-16 ***
ORIGIN_GRID_ID1937          1.645e+01  2.800e-03   5874.19   <2e-16 ***
ORIGIN_GRID_ID1940          1.831e+01  1.590e-03  11517.11   <2e-16 ***
ORIGIN_GRID_ID1941          1.729e+01  1.946e-03   8888.10   <2e-16 ***
ORIGIN_GRID_ID1942          1.688e+01  4.273e-03   3950.83   <2e-16 ***
ORIGIN_GRID_ID1955          1.715e+01  2.037e-03   8421.84   <2e-16 ***
ORIGIN_GRID_ID1959          1.685e+01  1.999e-03   8428.63   <2e-16 ***
ORIGIN_GRID_ID1960          1.715e+01  1.872e-03   9162.31   <2e-16 ***
ORIGIN_GRID_ID1962          1.692e+01  2.154e-03   7853.02   <2e-16 ***
ORIGIN_GRID_ID1963          1.615e+01  2.361e-03   6839.05   <2e-16 ***
ORIGIN_GRID_ID1967          1.843e+01  1.631e-03  11299.51   <2e-16 ***
ORIGIN_GRID_ID1968          1.857e+01  1.748e-03  10626.16   <2e-16 ***
ORIGIN_GRID_ID1985          1.537e+01  3.244e-03   4739.96   <2e-16 ***
ORIGIN_GRID_ID1987          1.761e+01  1.621e-03  10858.48   <2e-16 ***
ORIGIN_GRID_ID1988          1.615e+01  2.547e-03   6342.86   <2e-16 ***
ORIGIN_GRID_ID1989          1.642e+01  2.606e-03   6302.61   <2e-16 ***
ORIGIN_GRID_ID1990          1.813e+01  1.561e-03  11612.10   <2e-16 ***
ORIGIN_GRID_ID1994          1.651e+01  5.303e-03   3113.73   <2e-16 ***
ORIGIN_GRID_ID1995          1.871e+01  1.642e-03  11394.82   <2e-16 ***
ORIGIN_GRID_ID2010          1.540e+01  2.517e-03   6119.88   <2e-16 ***
ORIGIN_GRID_ID2011          1.646e+01  1.809e-03   9098.85   <2e-16 ***
ORIGIN_GRID_ID2012          1.555e+01  3.827e-03   4063.46   <2e-16 ***
ORIGIN_GRID_ID2013          1.643e+01  2.211e-03   7433.52   <2e-16 ***
ORIGIN_GRID_ID2014          1.675e+01  2.014e-03   8312.83   <2e-16 ***
ORIGIN_GRID_ID2015          1.677e+01  2.844e-03   5897.49   <2e-16 ***
ORIGIN_GRID_ID2016          1.695e+01  2.053e-03   8255.13   <2e-16 ***
ORIGIN_GRID_ID2017          1.694e+01  2.068e-03   8193.24   <2e-16 ***
ORIGIN_GRID_ID2021          1.686e+01  3.458e-03   4874.96   <2e-16 ***
ORIGIN_GRID_ID2038          1.570e+01  1.872e-03   8386.98   <2e-16 ***
ORIGIN_GRID_ID2039          1.722e+01  2.293e-03   7507.99   <2e-16 ***
ORIGIN_GRID_ID2040          1.738e+01  1.748e-03   9943.47   <2e-16 ***
ORIGIN_GRID_ID2041          1.823e+01  1.587e-03  11490.68   <2e-16 ***
ORIGIN_GRID_ID2042          1.675e+01  2.560e-03   6542.03   <2e-16 ***
ORIGIN_GRID_ID2043          1.548e+01  4.987e-03   3104.20   <2e-16 ***
ORIGIN_GRID_ID2044          1.795e+01  1.607e-03  11168.23   <2e-16 ***
ORIGIN_GRID_ID2064          1.337e+01  8.910e-03   1500.26   <2e-16 ***
ORIGIN_GRID_ID2065          1.562e+01  2.484e-03   6288.16   <2e-16 ***
ORIGIN_GRID_ID2066          1.596e+01  2.492e-03   6405.93   <2e-16 ***
ORIGIN_GRID_ID2067          1.729e+01  2.180e-03   7930.89   <2e-16 ***
ORIGIN_GRID_ID2068          1.736e+01  2.152e-03   8066.52   <2e-16 ***
ORIGIN_GRID_ID2070          1.746e+01  2.311e-03   7555.12   <2e-16 ***
ORIGIN_GRID_ID2071          1.682e+01  2.990e-03   5627.48   <2e-16 ***
ORIGIN_GRID_ID2093          1.591e+01  2.039e-03   7804.66   <2e-16 ***
ORIGIN_GRID_ID2094          1.707e+01  2.316e-03   7371.80   <2e-16 ***
ORIGIN_GRID_ID2095          1.772e+01  2.738e-03   6472.30   <2e-16 ***
ORIGIN_GRID_ID2098          1.597e+01  4.141e-03   3855.02   <2e-16 ***
ORIGIN_GRID_ID2119          1.637e+01  2.405e-03   6806.06   <2e-16 ***
ORIGIN_GRID_ID2120          1.608e+01  2.701e-03   5954.87   <2e-16 ***
ORIGIN_GRID_ID2123          1.661e+01  2.272e-03   7307.11   <2e-16 ***
ORIGIN_GRID_ID2147          1.648e+01  2.036e-03   8092.28   <2e-16 ***
ORIGIN_GRID_ID2148          1.746e+01  1.711e-03  10202.72   <2e-16 ***
ORIGIN_GRID_ID2149          1.664e+01  2.803e-03   5935.02   <2e-16 ***
ORIGIN_GRID_ID2150          1.528e+01  4.186e-03   3650.60   <2e-16 ***
ORIGIN_GRID_ID2151          1.626e+01  2.692e-03   6041.03   <2e-16 ***
ORIGIN_GRID_ID2152          1.719e+01  2.406e-03   7145.57   <2e-16 ***
ORIGIN_GRID_ID2154          1.656e+01  3.034e-03   5459.67   <2e-16 ***
ORIGIN_GRID_ID2174          1.594e+01  3.765e-03   4235.33   <2e-16 ***
ORIGIN_GRID_ID2177          1.793e+01  1.631e-03  10996.40   <2e-16 ***
ORIGIN_GRID_ID2178          1.704e+01  1.877e-03   9078.74   <2e-16 ***
ORIGIN_GRID_ID2179          1.737e+01  2.122e-03   8182.72   <2e-16 ***
ORIGIN_GRID_ID2180          1.710e+01  2.576e-03   6639.20   <2e-16 ***
ORIGIN_GRID_ID2201          1.709e+01  1.938e-03   8816.92   <2e-16 ***
ORIGIN_GRID_ID2203          1.684e+01  3.263e-03   5159.87   <2e-16 ***
ORIGIN_GRID_ID2204          1.579e+01  3.337e-03   4732.29   <2e-16 ***
ORIGIN_GRID_ID2205          1.630e+01  2.092e-03   7788.27   <2e-16 ***
ORIGIN_GRID_ID2206          1.830e+01  1.585e-03  11540.08   <2e-16 ***
ORIGIN_GRID_ID2208          1.773e+01  2.060e-03   8606.81   <2e-16 ***
ORIGIN_GRID_ID2228          1.662e+01  2.225e-03   7471.63   <2e-16 ***
ORIGIN_GRID_ID2231          1.670e+01  2.060e-03   8106.86   <2e-16 ***
ORIGIN_GRID_ID2233          1.829e+01  1.589e-03  11509.06   <2e-16 ***
ORIGIN_GRID_ID2234          1.461e+01  2.494e-02    585.80   <2e-16 ***
ORIGIN_GRID_ID2235          1.437e+01  2.054e-02    699.74   <2e-16 ***
ORIGIN_GRID_ID2254          1.550e+01  7.922e-03   1956.43   <2e-16 ***
ORIGIN_GRID_ID2255          1.689e+01  2.291e-03   7372.67   <2e-16 ***
ORIGIN_GRID_ID2256          1.653e+01  2.352e-03   7027.09   <2e-16 ***
ORIGIN_GRID_ID2257          1.529e+01  1.229e-02   1244.33   <2e-16 ***
ORIGIN_GRID_ID2259          1.552e+01  5.623e-03   2759.57   <2e-16 ***
ORIGIN_GRID_ID2260          1.779e+01  1.757e-03  10124.02   <2e-16 ***
ORIGIN_GRID_ID2261          1.799e+01  1.698e-03  10594.98   <2e-16 ***
ORIGIN_GRID_ID2262          1.684e+01  2.817e-03   5978.82   <2e-16 ***
ORIGIN_GRID_ID2281          1.680e+01  3.004e-03   5592.76   <2e-16 ***
ORIGIN_GRID_ID2282          1.637e+01  2.713e-03   6032.84   <2e-16 ***
ORIGIN_GRID_ID2283          1.702e+01  1.923e-03   8854.73   <2e-16 ***
ORIGIN_GRID_ID2285          1.771e+01  1.773e-03   9988.23   <2e-16 ***
ORIGIN_GRID_ID2286          1.642e+01  2.819e-03   5825.88   <2e-16 ***
ORIGIN_GRID_ID2287          1.828e+01  1.567e-03  11663.91   <2e-16 ***
ORIGIN_GRID_ID2288          1.596e+01  4.614e-03   3458.31   <2e-16 ***
ORIGIN_GRID_ID2310          1.655e+01  2.243e-03   7377.76   <2e-16 ***
ORIGIN_GRID_ID2312          1.469e+01  1.063e-02   1382.47   <2e-16 ***
ORIGIN_GRID_ID2313          1.701e+01  1.945e-03   8745.32   <2e-16 ***
ORIGIN_GRID_ID2314          1.750e+01  1.608e-03  10883.42   <2e-16 ***
ORIGIN_GRID_ID2315          1.686e+01  2.165e-03   7787.21   <2e-16 ***
ORIGIN_GRID_ID2316          1.792e+01  1.561e-03  11474.12   <2e-16 ***
ORIGIN_GRID_ID2335          1.459e+01  1.078e-02   1352.80   <2e-16 ***
ORIGIN_GRID_ID2339          1.688e+01  2.606e-03   6477.80   <2e-16 ***
ORIGIN_GRID_ID2340          1.767e+01  1.692e-03  10441.85   <2e-16 ***
ORIGIN_GRID_ID2341          1.731e+01  1.751e-03   9883.74   <2e-16 ***
ORIGIN_GRID_ID2342          1.665e+01  1.909e-03   8725.57   <2e-16 ***
ORIGIN_GRID_ID2343          1.677e+01  2.417e-03   6938.05   <2e-16 ***
ORIGIN_GRID_ID2363          1.628e+01  3.380e-03   4817.61   <2e-16 ***
ORIGIN_GRID_ID2367          1.675e+01  2.789e-03   6005.72   <2e-16 ***
ORIGIN_GRID_ID2368          1.746e+01  1.874e-03   9316.05   <2e-16 ***
ORIGIN_GRID_ID2369          1.701e+01  2.120e-03   8025.78   <2e-16 ***
ORIGIN_GRID_ID2370          1.742e+01  1.705e-03  10222.71   <2e-16 ***
ORIGIN_GRID_ID2371          1.743e+01  1.813e-03   9613.68   <2e-16 ***
ORIGIN_GRID_ID2390          1.645e+01  2.764e-03   5953.05   <2e-16 ***
ORIGIN_GRID_ID2391          1.647e+01  2.540e-03   6484.85   <2e-16 ***
ORIGIN_GRID_ID2394          1.591e+01  4.468e-03   3561.03   <2e-16 ***
ORIGIN_GRID_ID2395          1.792e+01  1.708e-03  10494.70   <2e-16 ***
ORIGIN_GRID_ID2396          1.746e+01  1.634e-03  10687.32   <2e-16 ***
ORIGIN_GRID_ID2397          1.657e+01  2.444e-03   6777.67   <2e-16 ***
ORIGIN_GRID_ID2398          1.690e+01  2.466e-03   6850.86   <2e-16 ***
ORIGIN_GRID_ID2418          1.655e+01  3.092e-03   5354.10   <2e-16 ***
ORIGIN_GRID_ID2419          1.586e+01  4.074e-03   3893.49   <2e-16 ***
ORIGIN_GRID_ID2422          1.644e+01  6.286e-03   2615.05   <2e-16 ***
ORIGIN_GRID_ID2423          1.678e+01  2.554e-03   6569.90   <2e-16 ***
ORIGIN_GRID_ID2424          1.774e+01  1.583e-03  11201.63   <2e-16 ***
ORIGIN_GRID_ID2425          1.719e+01  1.842e-03   9335.95   <2e-16 ***
ORIGIN_GRID_ID2426          1.646e+01  3.723e-03   4420.65   <2e-16 ***
ORIGIN_GRID_ID2443          1.707e+01  2.220e-03   7688.07   <2e-16 ***
ORIGIN_GRID_ID2445          1.731e+01  1.841e-03   9400.58   <2e-16 ***
ORIGIN_GRID_ID2449          1.743e+01  3.077e-03   5665.32   <2e-16 ***
ORIGIN_GRID_ID2450          1.723e+01  1.997e-03   8626.69   <2e-16 ***
ORIGIN_GRID_ID2451          1.769e+01  1.659e-03  10659.93   <2e-16 ***
ORIGIN_GRID_ID2472          1.508e+01  1.801e-02    837.57   <2e-16 ***
ORIGIN_GRID_ID2473          1.709e+01  2.368e-03   7217.05   <2e-16 ***
ORIGIN_GRID_ID2478          1.681e+01  2.210e-03   7608.20   <2e-16 ***
ORIGIN_GRID_ID2479          1.553e+01  5.926e-03   2621.09   <2e-16 ***
ORIGIN_GRID_ID2497          1.737e+01  2.014e-03   8623.80   <2e-16 ***
ORIGIN_GRID_ID2499          1.758e+01  2.327e-03   7555.43   <2e-16 ***
ORIGIN_GRID_ID2505          1.695e+01  2.353e-03   7200.60   <2e-16 ***
ORIGIN_GRID_ID2527          1.744e+01  2.012e-03   8670.51   <2e-16 ***
ORIGIN_GRID_ID2532          1.700e+01  2.584e-03   6577.46   <2e-16 ***
ORIGIN_GRID_ID2533          1.724e+01  3.092e-03   5575.67   <2e-16 ***
ORIGIN_GRID_ID2551          1.681e+01  2.924e-03   5750.54   <2e-16 ***
ORIGIN_GRID_ID2553          1.693e+01  4.120e-03   4108.73   <2e-16 ***
ORIGIN_GRID_ID2554          1.560e+01  6.322e-03   2467.22   <2e-16 ***
ORIGIN_GRID_ID2559          1.699e+01  2.977e-03   5707.37   <2e-16 ***
ORIGIN_GRID_ID2580          1.747e+01  2.031e-03   8604.60   <2e-16 ***
ORIGIN_GRID_ID2581          1.670e+01  3.691e-03   4523.68   <2e-16 ***
ORIGIN_GRID_ID2607          1.803e+01  1.660e-03  10863.27   <2e-16 ***
ORIGIN_GRID_ID2608          1.637e+01  3.940e-03   4155.99   <2e-16 ***
ORIGIN_GRID_ID2634          1.785e+01  1.814e-03   9839.12   <2e-16 ***
ORIGIN_GRID_ID2635          1.795e+01  2.037e-03   8811.23   <2e-16 ***
ORIGIN_GRID_ID2636          1.739e+01  2.312e-03   7519.05   <2e-16 ***
ORIGIN_GRID_ID2661          1.738e+01  1.846e-03   9412.76   <2e-16 ***
ORIGIN_GRID_ID2663          1.800e+01  1.616e-03  11138.40   <2e-16 ***
ORIGIN_GRID_ID2665          1.708e+01  2.670e-03   6395.30   <2e-16 ***
ORIGIN_GRID_ID2688          1.743e+01  1.954e-03   8920.96   <2e-16 ***
ORIGIN_GRID_ID2689          1.744e+01  2.065e-03   8446.07   <2e-16 ***
ORIGIN_GRID_ID2690          1.645e+01  2.579e-03   6378.81   <2e-16 ***
ORIGIN_GRID_ID2691          1.813e+01  1.651e-03  10985.91   <2e-16 ***
ORIGIN_GRID_ID2693          1.779e+01  1.912e-03   9304.05   <2e-16 ***
ORIGIN_GRID_ID2715          1.793e+01  1.940e-03   9240.04   <2e-16 ***
ORIGIN_GRID_ID2717          1.671e+01  1.929e-03   8659.89   <2e-16 ***
ORIGIN_GRID_ID2718          1.721e+01  2.540e-03   6777.18   <2e-16 ***
ORIGIN_GRID_ID2719          1.806e+01  1.652e-03  10930.66   <2e-16 ***
ORIGIN_GRID_ID2742          1.722e+01  2.404e-03   7162.45   <2e-16 ***
ORIGIN_GRID_ID2743          1.619e+01  5.076e-03   3189.61   <2e-16 ***
ORIGIN_GRID_ID2744          1.700e+01  2.001e-03   8496.97   <2e-16 ***
ORIGIN_GRID_ID2745          1.694e+01  1.888e-03   8970.73   <2e-16 ***
ORIGIN_GRID_ID2747          1.699e+01  2.402e-03   7074.12   <2e-16 ***
ORIGIN_GRID_ID2768          1.756e+01  2.228e-03   7882.06   <2e-16 ***
ORIGIN_GRID_ID2771          1.770e+01  1.715e-03  10323.41   <2e-16 ***
ORIGIN_GRID_ID2773          1.731e+01  1.980e-03   8744.94   <2e-16 ***
ORIGIN_GRID_ID2798          1.644e+01  2.921e-03   5629.31   <2e-16 ***
ORIGIN_GRID_ID2799          1.718e+01  1.787e-03   9614.94   <2e-16 ***
ORIGIN_GRID_ID2800          1.727e+01  2.043e-03   8456.05   <2e-16 ***
ORIGIN_GRID_ID2824          1.646e+01  2.878e-03   5721.21   <2e-16 ***
ORIGIN_GRID_ID2825          1.724e+01  1.718e-03  10034.79   <2e-16 ***
ORIGIN_GRID_ID2826          1.736e+01  2.263e-03   7672.85   <2e-16 ***
ORIGIN_GRID_ID2827          1.759e+01  1.917e-03   9175.81   <2e-16 ***
ORIGIN_GRID_ID2852          1.746e+01  1.973e-03   8853.00   <2e-16 ***
ORIGIN_GRID_ID2853          1.744e+01  1.671e-03  10431.68   <2e-16 ***
ORIGIN_GRID_ID2854          1.795e+01  1.716e-03  10458.54   <2e-16 ***
ORIGIN_GRID_ID2878          1.684e+01  2.784e-03   6048.49   <2e-16 ***
ORIGIN_GRID_ID2879          1.717e+01  2.045e-03   8396.75   <2e-16 ***
ORIGIN_GRID_ID2880          1.718e+01  2.060e-03   8339.26   <2e-16 ***
ORIGIN_GRID_ID2881          1.845e+01  1.753e-03  10527.20   <2e-16 ***
ORIGIN_GRID_ID2907          1.722e+01  2.401e-03   7170.39   <2e-16 ***
ORIGIN_GRID_ID2908          1.767e+01  2.010e-03   8788.68   <2e-16 ***
ORIGIN_GRID_ID2933          1.535e+01  7.912e-03   1939.79   <2e-16 ***
ORIGIN_GRID_ID2934          1.693e+01  2.565e-03   6601.50   <2e-16 ***
ORIGIN_GRID_ID3098          1.668e+01  5.418e-03   3079.79   <2e-16 ***
log(TDESTIN_BIZ_COUNT)      3.192e-02  1.004e-04    317.76   <2e-16 ***
log(TDESTIN_FINSERV_COUNT)  2.525e-01  9.292e-05   2717.07   <2e-16 ***
log(TDESTIN_MRTEXIT_COUNT)  6.729e-01  1.470e-04   4577.84   <2e-16 ***
log(TDESTIN_BUSSTOP_COUNT)  8.802e-02  2.470e-04    356.29   <2e-16 ***
log(TDESTIN_HDBCOMM_UNITS)  3.431e-02  5.947e-05    577.04   <2e-16 ***
log(TDESTIN_HDBRES_UNITS)  -9.273e-03  1.391e-04    -66.64   <2e-16 ***
log(TDESTIN_SCHOOLS_COUNT)  3.265e-01  2.260e-04   1444.87   <2e-16 ***
log(DISTANCE)              -1.479e+00  1.267e-04 -11675.49   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2954357158  on 101715  degrees of freedom
Residual deviance:  153161913  on 101359  degrees of freedom
AIC: 153920852

Number of Fisher Scoring iterations: 6
CalcRSquared(orcSIM_Poisson2$data$TRIPS, orcSIM_Poisson2$fitted.values)
[1] 0.6282076
decSIM_Poisson2 <- glm(formula = TRIPS ~ 
                DESTIN_GRID_ID +
                log(TORIGIN_BIZ_COUNT) +
                log(TORIGIN_FINSERV_COUNT) +
                  log(TORIGIN_MRTEXIT_COUNT) +
                  log(TORIGIN_BUSSTOP_COUNT) +
                  log(TORIGIN_HDBCOMM_UNITS) +
                  log(TORIGIN_HDBRES_UNITS) + 
                  log(TORIGIN_SCHOOLS_COUNT) + 
                log(DISTANCE) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow,
              na.action = na.exclude)
summary(decSIM_Poisson2)

Call:
glm(formula = TRIPS ~ DESTIN_GRID_ID + log(TORIGIN_BIZ_COUNT) + 
    log(TORIGIN_FINSERV_COUNT) + log(TORIGIN_MRTEXIT_COUNT) + 
    log(TORIGIN_BUSSTOP_COUNT) + log(TORIGIN_HDBCOMM_UNITS) + 
    log(TORIGIN_HDBRES_UNITS) + log(TORIGIN_SCHOOLS_COUNT) + 
    log(DISTANCE) - 1, family = poisson(link = "log"), data = inter_zonal_flow, 
    na.action = na.exclude)

Coefficients:
                             Estimate Std. Error    z value Pr(>|z|)    
DESTIN_GRID_ID664           1.415e+01  4.595e-03   3079.664  < 2e-16 ***
DESTIN_GRID_ID718           1.397e+01  1.976e-03   7073.503  < 2e-16 ***
DESTIN_GRID_ID745           1.238e+01  3.086e-03   4011.556  < 2e-16 ***
DESTIN_GRID_ID746           1.324e+01  2.389e-03   5542.057  < 2e-16 ***
DESTIN_GRID_ID772           1.443e+01  1.631e-03   8848.587  < 2e-16 ***
DESTIN_GRID_ID799           1.450e+01  1.852e-03   7827.426  < 2e-16 ***
DESTIN_GRID_ID800           1.332e+01  1.958e-03   6801.942  < 2e-16 ***
DESTIN_GRID_ID826           1.553e+01  1.577e-03   9843.445  < 2e-16 ***
DESTIN_GRID_ID827           1.421e+01  2.153e-03   6599.806  < 2e-16 ***
DESTIN_GRID_ID854           1.301e+01  2.599e-03   5006.873  < 2e-16 ***
DESTIN_GRID_ID880           1.246e+01  3.594e-03   3467.119  < 2e-16 ***
DESTIN_GRID_ID881           1.303e+01  3.611e-03   3608.006  < 2e-16 ***
DESTIN_GRID_ID908           1.341e+01  2.126e-03   6306.975  < 2e-16 ***
DESTIN_GRID_ID934           1.377e+01  2.038e-03   6754.275  < 2e-16 ***
DESTIN_GRID_ID935           1.342e+01  2.286e-03   5872.370  < 2e-16 ***
DESTIN_GRID_ID961           1.331e+01  2.499e-03   5325.117  < 2e-16 ***
DESTIN_GRID_ID962           1.540e+01  1.574e-03   9783.981  < 2e-16 ***
DESTIN_GRID_ID987           1.438e+01  1.834e-03   7840.375  < 2e-16 ***
DESTIN_GRID_ID988           1.244e+01  3.427e-03   3631.070  < 2e-16 ***
DESTIN_GRID_ID989           1.358e+01  2.131e-03   6374.454  < 2e-16 ***
DESTIN_GRID_ID1015          1.113e+01  8.499e-03   1309.385  < 2e-16 ***
DESTIN_GRID_ID1016          1.273e+01  2.659e-03   4786.434  < 2e-16 ***
DESTIN_GRID_ID1043          1.336e+01  3.087e-03   4328.780  < 2e-16 ***
DESTIN_GRID_ID1068          1.142e+01  2.065e-02    552.876  < 2e-16 ***
DESTIN_GRID_ID1070          1.365e+01  1.999e-03   6829.933  < 2e-16 ***
DESTIN_GRID_ID1096          1.323e+01  2.160e-03   6126.971  < 2e-16 ***
DESTIN_GRID_ID1097          1.285e+01  2.999e-03   4285.910  < 2e-16 ***
DESTIN_GRID_ID1099          1.353e+01  2.147e-03   6301.307  < 2e-16 ***
DESTIN_GRID_ID1122          1.397e+01  2.472e-03   5654.110  < 2e-16 ***
DESTIN_GRID_ID1123          1.497e+01  1.620e-03   9237.127  < 2e-16 ***
DESTIN_GRID_ID1124          1.352e+01  2.146e-03   6300.176  < 2e-16 ***
DESTIN_GRID_ID1125          1.284e+01  2.976e-03   4315.525  < 2e-16 ***
DESTIN_GRID_ID1127          1.306e+01  2.347e-03   5562.753  < 2e-16 ***
DESTIN_GRID_ID1128          1.374e+01  2.744e-03   5006.166  < 2e-16 ***
DESTIN_GRID_ID1148          1.314e+01  3.192e-03   4117.187  < 2e-16 ***
DESTIN_GRID_ID1150          1.358e+01  2.049e-03   6628.052  < 2e-16 ***
DESTIN_GRID_ID1151          1.303e+01  2.359e-03   5523.202  < 2e-16 ***
DESTIN_GRID_ID1152          1.274e+01  3.522e-03   3618.526  < 2e-16 ***
DESTIN_GRID_ID1153          1.345e+01  2.219e-03   6061.444  < 2e-16 ***
DESTIN_GRID_ID1154          1.511e+01  1.645e-03   9182.898  < 2e-16 ***
DESTIN_GRID_ID1155          1.046e+01  1.727e-02    605.417  < 2e-16 ***
DESTIN_GRID_ID1176          1.406e+01  2.035e-03   6908.715  < 2e-16 ***
DESTIN_GRID_ID1178          1.296e+01  2.270e-03   5706.684  < 2e-16 ***
DESTIN_GRID_ID1179          1.221e+01  3.325e-03   3670.995  < 2e-16 ***
DESTIN_GRID_ID1180          1.067e+01  1.021e-02   1045.274  < 2e-16 ***
DESTIN_GRID_ID1181          1.379e+01  1.862e-03   7406.457  < 2e-16 ***
DESTIN_GRID_ID1182          1.331e+01  2.358e-03   5642.817  < 2e-16 ***
DESTIN_GRID_ID1183          1.319e+01  5.061e-03   2606.611  < 2e-16 ***
DESTIN_GRID_ID1205          1.458e+01  1.656e-03   8805.621  < 2e-16 ***
DESTIN_GRID_ID1206          1.340e+01  2.356e-03   5685.507  < 2e-16 ***
DESTIN_GRID_ID1207          1.321e+01  2.539e-03   5202.687  < 2e-16 ***
DESTIN_GRID_ID1209          1.486e+01  1.786e-03   8321.648  < 2e-16 ***
DESTIN_GRID_ID1232          1.381e+01  1.926e-03   7168.724  < 2e-16 ***
DESTIN_GRID_ID1233          1.441e+01  2.242e-03   6429.487  < 2e-16 ***
DESTIN_GRID_ID1235          1.416e+01  2.000e-03   7079.689  < 2e-16 ***
DESTIN_GRID_ID1255          1.420e+01  5.671e-03   2504.065  < 2e-16 ***
DESTIN_GRID_ID1258          1.452e+01  2.027e-03   7165.257  < 2e-16 ***
DESTIN_GRID_ID1259          1.304e+01  2.757e-03   4731.521  < 2e-16 ***
DESTIN_GRID_ID1261          1.293e+01  2.536e-03   5097.904  < 2e-16 ***
DESTIN_GRID_ID1262          1.341e+01  2.190e-03   6124.060  < 2e-16 ***
DESTIN_GRID_ID1283          1.316e+01  2.789e-03   4720.115  < 2e-16 ***
DESTIN_GRID_ID1284          1.275e+01  4.688e-03   2719.754  < 2e-16 ***
DESTIN_GRID_ID1286          1.213e+01  4.575e-03   2651.116  < 2e-16 ***
DESTIN_GRID_ID1289          1.389e+01  1.781e-03   7794.942  < 2e-16 ***
DESTIN_GRID_ID1309          1.433e+01  2.171e-03   6602.358  < 2e-16 ***
DESTIN_GRID_ID1310          1.502e+01  1.635e-03   9182.929  < 2e-16 ***
DESTIN_GRID_ID1315          1.464e+01  1.674e-03   8743.737  < 2e-16 ***
DESTIN_GRID_ID1316          1.239e+01  3.722e-03   3327.739  < 2e-16 ***
DESTIN_GRID_ID1337          1.332e+01  2.184e-03   6097.155  < 2e-16 ***
DESTIN_GRID_ID1338          1.256e+01  5.832e-03   2154.091  < 2e-16 ***
DESTIN_GRID_ID1343          1.241e+01  2.944e-03   4217.494  < 2e-16 ***
DESTIN_GRID_ID1363          1.410e+01  2.495e-03   5650.164  < 2e-16 ***
DESTIN_GRID_ID1364          1.287e+01  3.011e-03   4274.374  < 2e-16 ***
DESTIN_GRID_ID1366          1.331e+01  2.886e-03   4612.093  < 2e-16 ***
DESTIN_GRID_ID1369          1.349e+01  2.197e-03   6140.051  < 2e-16 ***
DESTIN_GRID_ID1370          1.332e+01  2.426e-03   5489.270  < 2e-16 ***
DESTIN_GRID_ID1374          1.270e+01  3.242e-03   3915.867  < 2e-16 ***
DESTIN_GRID_ID1375          1.308e+01  5.624e-03   2325.202  < 2e-16 ***
DESTIN_GRID_ID1391          1.296e+01  4.009e-03   3233.540  < 2e-16 ***
DESTIN_GRID_ID1392          1.185e+01  6.545e-03   1810.072  < 2e-16 ***
DESTIN_GRID_ID1396          1.176e+01  8.298e-03   1417.217  < 2e-16 ***
DESTIN_GRID_ID1397          1.294e+01  2.669e-03   4849.509  < 2e-16 ***
DESTIN_GRID_ID1401          1.453e+01  1.865e-03   7789.590  < 2e-16 ***
DESTIN_GRID_ID1402          1.359e+01  2.154e-03   6310.255  < 2e-16 ***
DESTIN_GRID_ID1423          1.305e+01  4.293e-03   3038.636  < 2e-16 ***
DESTIN_GRID_ID1428          1.300e+01  2.708e-03   4801.931  < 2e-16 ***
DESTIN_GRID_ID1429          1.364e+01  2.894e-03   4712.270  < 2e-16 ***
DESTIN_GRID_ID1455          1.287e+01  2.758e-03   4667.419  < 2e-16 ***
DESTIN_GRID_ID1456          1.312e+01  2.552e-03   5140.389  < 2e-16 ***
DESTIN_GRID_ID1471          1.357e+01  2.980e-03   4552.754  < 2e-16 ***
DESTIN_GRID_ID1482          1.449e+01  1.783e-03   8126.238  < 2e-16 ***
DESTIN_GRID_ID1499          1.274e+01  4.673e-03   2725.822  < 2e-16 ***
DESTIN_GRID_ID1509          1.238e+01  4.745e-03   2608.260  < 2e-16 ***
DESTIN_GRID_ID1510          1.529e+01  1.601e-03   9551.437  < 2e-16 ***
DESTIN_GRID_ID1525          1.407e+01  1.904e-03   7389.916  < 2e-16 ***
DESTIN_GRID_ID1536          1.384e+01  1.854e-03   7467.006  < 2e-16 ***
DESTIN_GRID_ID1537          1.394e+01  2.738e-03   5092.364  < 2e-16 ***
DESTIN_GRID_ID1552          1.157e+01  9.412e-03   1228.807  < 2e-16 ***
DESTIN_GRID_ID1553          1.299e+01  3.213e-03   4041.289  < 2e-16 ***
DESTIN_GRID_ID1563          1.364e+01  2.446e-03   5576.709  < 2e-16 ***
DESTIN_GRID_ID1564          1.367e+01  1.855e-03   7370.226  < 2e-16 ***
DESTIN_GRID_ID1578          1.169e+01  6.337e-03   1844.346  < 2e-16 ***
DESTIN_GRID_ID1579          1.384e+01  2.160e-03   6407.308  < 2e-16 ***
DESTIN_GRID_ID1590          1.338e+01  2.141e-03   6249.700  < 2e-16 ***
DESTIN_GRID_ID1591          1.382e+01  2.131e-03   6484.989  < 2e-16 ***
DESTIN_GRID_ID1605          1.329e+01  2.503e-03   5311.197  < 2e-16 ***
DESTIN_GRID_ID1606          1.326e+01  2.577e-03   5143.998  < 2e-16 ***
DESTIN_GRID_ID1617          1.220e+01  6.541e-03   1865.688  < 2e-16 ***
DESTIN_GRID_ID1618          1.519e+01  1.623e-03   9360.940  < 2e-16 ***
DESTIN_GRID_ID1631          1.290e+01  3.196e-03   4037.303  < 2e-16 ***
DESTIN_GRID_ID1632          1.300e+01  2.666e-03   4875.988  < 2e-16 ***
DESTIN_GRID_ID1634          1.298e+01  4.425e-03   2934.094  < 2e-16 ***
DESTIN_GRID_ID1644          1.347e+01  2.461e-03   5473.222  < 2e-16 ***
DESTIN_GRID_ID1645          1.392e+01  2.052e-03   6784.468  < 2e-16 ***
DESTIN_GRID_ID1658          1.281e+01  3.319e-03   3858.864  < 2e-16 ***
DESTIN_GRID_ID1659          1.357e+01  2.030e-03   6683.115  < 2e-16 ***
DESTIN_GRID_ID1672          1.339e+01  3.541e-03   3782.919  < 2e-16 ***
DESTIN_GRID_ID1684          1.348e+01  2.443e-03   5515.684  < 2e-16 ***
DESTIN_GRID_ID1685          1.319e+01  3.442e-03   3831.128  < 2e-16 ***
DESTIN_GRID_ID1686          1.321e+01  2.487e-03   5310.316  < 2e-16 ***
DESTIN_GRID_ID1688          1.266e+01  5.943e-03   2130.103  < 2e-16 ***
DESTIN_GRID_ID1699          1.355e+01  2.212e-03   6125.723  < 2e-16 ***
DESTIN_GRID_ID1700          1.310e+01  5.999e-03   2184.079  < 2e-16 ***
DESTIN_GRID_ID1712          1.211e+01  3.983e-03   3040.855  < 2e-16 ***
DESTIN_GRID_ID1713          1.394e+01  1.841e-03   7570.374  < 2e-16 ***
DESTIN_GRID_ID1727          1.374e+01  2.012e-03   6830.314  < 2e-16 ***
DESTIN_GRID_ID1739          1.405e+01  1.759e-03   7985.015  < 2e-16 ***
DESTIN_GRID_ID1753          1.506e+01  1.591e-03   9465.109  < 2e-16 ***
DESTIN_GRID_ID1754          1.323e+01  2.753e-03   4805.796  < 2e-16 ***
DESTIN_GRID_ID1766          1.350e+01  2.003e-03   6741.670  < 2e-16 ***
DESTIN_GRID_ID1767          1.350e+01  1.937e-03   6966.423  < 2e-16 ***
DESTIN_GRID_ID1780          1.295e+01  1.006e-02   1287.705  < 2e-16 ***
DESTIN_GRID_ID1781          1.325e+01  2.384e-03   5557.804  < 2e-16 ***
DESTIN_GRID_ID1792          1.259e+01  3.060e-03   4114.127  < 2e-16 ***
DESTIN_GRID_ID1793          1.377e+01  1.857e-03   7413.934  < 2e-16 ***
DESTIN_GRID_ID1794          1.270e+01  3.568e-03   3557.889  < 2e-16 ***
DESTIN_GRID_ID1807          1.205e+01  3.416e-03   3526.782  < 2e-16 ***
DESTIN_GRID_ID1820          1.292e+01  2.779e-03   4649.221  < 2e-16 ***
DESTIN_GRID_ID1821          1.446e+01  1.702e-03   8499.581  < 2e-16 ***
DESTIN_GRID_ID1833          1.401e+01  1.765e-03   7938.832  < 2e-16 ***
DESTIN_GRID_ID1835          1.237e+01  3.639e-03   3400.065  < 2e-16 ***
DESTIN_GRID_ID1847          1.170e+01  9.244e-03   1265.890  < 2e-16 ***
DESTIN_GRID_ID1854          1.305e+01  3.548e-03   3677.248  < 2e-16 ***
DESTIN_GRID_ID1859          1.280e+01  2.201e-03   5816.394  < 2e-16 ***
DESTIN_GRID_ID1860          1.305e+01  2.283e-03   5714.365  < 2e-16 ***
DESTIN_GRID_ID1861          1.279e+01  3.488e-03   3667.444  < 2e-16 ***
DESTIN_GRID_ID1874          1.327e+01  2.445e-03   5426.926  < 2e-16 ***
DESTIN_GRID_ID1875          1.363e+01  1.967e-03   6932.424  < 2e-16 ***
DESTIN_GRID_ID1882          1.386e+01  2.036e-03   6809.509  < 2e-16 ***
DESTIN_GRID_ID1883          1.245e+01  3.781e-03   3293.197  < 2e-16 ***
DESTIN_GRID_ID1886          1.529e+01  1.610e-03   9496.111  < 2e-16 ***
DESTIN_GRID_ID1887          1.514e+01  1.560e-03   9700.926  < 2e-16 ***
DESTIN_GRID_ID1888          1.288e+01  3.491e-03   3690.027  < 2e-16 ***
DESTIN_GRID_ID1905          1.241e+01  3.955e-03   3138.656  < 2e-16 ***
DESTIN_GRID_ID1907          1.333e+01  2.540e-03   5248.755  < 2e-16 ***
DESTIN_GRID_ID1908          1.266e+01  3.240e-03   3907.326  < 2e-16 ***
DESTIN_GRID_ID1909          1.304e+01  2.487e-03   5241.964  < 2e-16 ***
DESTIN_GRID_ID1912          9.951e+00  2.099e-02    474.112  < 2e-16 ***
DESTIN_GRID_ID1913          1.315e+01  2.159e-03   6092.767  < 2e-16 ***
DESTIN_GRID_ID1914          1.380e+01  1.956e-03   7055.263  < 2e-16 ***
DESTIN_GRID_ID1928          1.321e+01  2.975e-03   4439.677  < 2e-16 ***
DESTIN_GRID_ID1929          1.317e+01  3.093e-03   4258.696  < 2e-16 ***
DESTIN_GRID_ID1933          1.398e+01  2.045e-03   6837.059  < 2e-16 ***
DESTIN_GRID_ID1935          1.341e+01  2.490e-03   5384.650  < 2e-16 ***
DESTIN_GRID_ID1936          1.331e+01  2.426e-03   5488.463  < 2e-16 ***
DESTIN_GRID_ID1937          1.325e+01  2.495e-03   5309.243  < 2e-16 ***
DESTIN_GRID_ID1940          1.307e+01  2.368e-03   5519.361  < 2e-16 ***
DESTIN_GRID_ID1941          1.231e+01  3.320e-03   3706.837  < 2e-16 ***
DESTIN_GRID_ID1942          1.336e+01  4.578e-03   2917.574  < 2e-16 ***
DESTIN_GRID_ID1955          1.403e+01  2.070e-03   6775.335  < 2e-16 ***
DESTIN_GRID_ID1959          1.371e+01  2.114e-03   6482.620  < 2e-16 ***
DESTIN_GRID_ID1960          1.398e+01  1.856e-03   7535.206  < 2e-16 ***
DESTIN_GRID_ID1962          1.286e+01  2.633e-03   4883.878  < 2e-16 ***
DESTIN_GRID_ID1963          1.278e+01  2.483e-03   5145.700  < 2e-16 ***
DESTIN_GRID_ID1967          1.350e+01  2.164e-03   6238.184  < 2e-16 ***
DESTIN_GRID_ID1968          1.352e+01  2.573e-03   5254.616  < 2e-16 ***
DESTIN_GRID_ID1985          1.356e+01  2.698e-03   5026.844  < 2e-16 ***
DESTIN_GRID_ID1987          1.472e+01  1.630e-03   9031.111  < 2e-16 ***
DESTIN_GRID_ID1988          1.259e+01  2.800e-03   4497.557  < 2e-16 ***
DESTIN_GRID_ID1989          1.243e+01  3.192e-03   3895.061  < 2e-16 ***
DESTIN_GRID_ID1990          1.498e+01  1.582e-03   9466.016  < 2e-16 ***
DESTIN_GRID_ID1994          1.100e+01  1.249e-02    880.348  < 2e-16 ***
DESTIN_GRID_ID1995          1.298e+01  2.702e-03   4804.313  < 2e-16 ***
DESTIN_GRID_ID2010          1.369e+01  1.912e-03   7162.171  < 2e-16 ***
DESTIN_GRID_ID2011          1.372e+01  2.144e-03   6399.768  < 2e-16 ***
DESTIN_GRID_ID2012          1.290e+01  3.237e-03   3986.087  < 2e-16 ***
DESTIN_GRID_ID2013          1.304e+01  2.190e-03   5953.992  < 2e-16 ***
DESTIN_GRID_ID2014          1.317e+01  2.083e-03   6323.687  < 2e-16 ***
DESTIN_GRID_ID2015          1.359e+01  2.624e-03   5176.849  < 2e-16 ***
DESTIN_GRID_ID2016          1.317e+01  2.297e-03   5733.871  < 2e-16 ***
DESTIN_GRID_ID2017          1.322e+01  2.271e-03   5818.572  < 2e-16 ***
DESTIN_GRID_ID2021          1.168e+01  6.500e-03   1796.333  < 2e-16 ***
DESTIN_GRID_ID2038          1.437e+01  1.717e-03   8369.071  < 2e-16 ***
DESTIN_GRID_ID2039          1.283e+01  3.216e-03   3988.567  < 2e-16 ***
DESTIN_GRID_ID2040          1.306e+01  2.442e-03   5349.309  < 2e-16 ***
DESTIN_GRID_ID2041          1.379e+01  1.912e-03   7210.272  < 2e-16 ***
DESTIN_GRID_ID2042          1.278e+01  3.147e-03   4060.266  < 2e-16 ***
DESTIN_GRID_ID2043          1.357e+01  2.505e-03   5418.461  < 2e-16 ***
DESTIN_GRID_ID2044          1.346e+01  2.039e-03   6602.525  < 2e-16 ***
DESTIN_GRID_ID2064          1.347e+01  2.592e-03   5196.147  < 2e-16 ***
DESTIN_GRID_ID2065          1.325e+01  2.567e-03   5162.428  < 2e-16 ***
DESTIN_GRID_ID2066          1.330e+01  2.056e-03   6466.334  < 2e-16 ***
DESTIN_GRID_ID2067          1.266e+01  3.130e-03   4042.720  < 2e-16 ***
DESTIN_GRID_ID2068          1.311e+01  2.680e-03   4890.492  < 2e-16 ***
DESTIN_GRID_ID2070          1.359e+01  2.622e-03   5184.237  < 2e-16 ***
DESTIN_GRID_ID2071          1.366e+01  2.323e-03   5879.817  < 2e-16 ***
DESTIN_GRID_ID2093          1.363e+01  1.932e-03   7053.181  < 2e-16 ***
DESTIN_GRID_ID2094          1.352e+01  2.138e-03   6323.943  < 2e-16 ***
DESTIN_GRID_ID2095          1.348e+01  3.041e-03   4431.788  < 2e-16 ***
DESTIN_GRID_ID2098          1.332e+01  2.829e-03   4708.138  < 2e-16 ***
DESTIN_GRID_ID2119          1.338e+01  2.533e-03   5282.480  < 2e-16 ***
DESTIN_GRID_ID2120          1.405e+01  2.035e-03   6902.384  < 2e-16 ***
DESTIN_GRID_ID2123          1.248e+01  3.320e-03   3760.495  < 2e-16 ***
DESTIN_GRID_ID2147          1.359e+01  2.075e-03   6552.479  < 2e-16 ***
DESTIN_GRID_ID2148          1.334e+01  2.151e-03   6202.928  < 2e-16 ***
DESTIN_GRID_ID2149          1.386e+01  2.358e-03   5877.814  < 2e-16 ***
DESTIN_GRID_ID2150          1.161e+01  5.985e-03   1940.660  < 2e-16 ***
DESTIN_GRID_ID2151          1.176e+01  5.189e-03   2266.838  < 2e-16 ***
DESTIN_GRID_ID2152          1.415e+01  1.975e-03   7165.145  < 2e-16 ***
DESTIN_GRID_ID2154          1.203e+01  4.649e-03   2587.927  < 2e-16 ***
DESTIN_GRID_ID2174          1.193e+01  4.820e-03   2475.605  < 2e-16 ***
DESTIN_GRID_ID2177          1.531e+01  1.541e-03   9930.780  < 2e-16 ***
DESTIN_GRID_ID2178          1.234e+01  2.834e-03   4355.643  < 2e-16 ***
DESTIN_GRID_ID2179          1.365e+01  2.141e-03   6376.949  < 2e-16 ***
DESTIN_GRID_ID2180          1.267e+01  3.642e-03   3477.575  < 2e-16 ***
DESTIN_GRID_ID2201          1.326e+01  2.429e-03   5458.271  < 2e-16 ***
DESTIN_GRID_ID2203          1.314e+01  3.591e-03   3660.155  < 2e-16 ***
DESTIN_GRID_ID2204          1.348e+01  2.450e-03   5502.465  < 2e-16 ***
DESTIN_GRID_ID2205          1.280e+01  2.406e-03   5319.204  < 2e-16 ***
DESTIN_GRID_ID2206          1.371e+01  1.861e-03   7365.638  < 2e-16 ***
DESTIN_GRID_ID2208          1.316e+01  2.636e-03   4993.227  < 2e-16 ***
DESTIN_GRID_ID2228          1.293e+01  2.696e-03   4797.102  < 2e-16 ***
DESTIN_GRID_ID2231          1.308e+01  2.366e-03   5528.759  < 2e-16 ***
DESTIN_GRID_ID2233          1.364e+01  1.826e-03   7468.687  < 2e-16 ***
DESTIN_GRID_ID2234          7.526e+00  9.130e-02     82.431  < 2e-16 ***
DESTIN_GRID_ID2235          1.066e+01  3.132e-02    340.313  < 2e-16 ***
DESTIN_GRID_ID2254          1.333e+01  5.669e-03   2351.401  < 2e-16 ***
DESTIN_GRID_ID2255          1.266e+01  4.081e-03   3101.768  < 2e-16 ***
DESTIN_GRID_ID2256          1.302e+01  2.575e-03   5055.732  < 2e-16 ***
DESTIN_GRID_ID2257          1.284e+01  7.745e-03   1657.494  < 2e-16 ***
DESTIN_GRID_ID2259          1.229e+01  4.370e-03   2812.983  < 2e-16 ***
DESTIN_GRID_ID2260          1.287e+01  2.292e-03   5615.539  < 2e-16 ***
DESTIN_GRID_ID2261          1.291e+01  2.291e-03   5634.859  < 2e-16 ***
DESTIN_GRID_ID2262          1.191e+01  4.894e-03   2434.008  < 2e-16 ***
DESTIN_GRID_ID2281          1.285e+01  3.945e-03   3256.339  < 2e-16 ***
DESTIN_GRID_ID2282          1.406e+01  1.933e-03   7273.519  < 2e-16 ***
DESTIN_GRID_ID2283          1.283e+01  2.713e-03   4729.537  < 2e-16 ***
DESTIN_GRID_ID2285          1.358e+01  2.191e-03   6199.267  < 2e-16 ***
DESTIN_GRID_ID2286          1.273e+01  2.765e-03   4603.093  < 2e-16 ***
DESTIN_GRID_ID2287          1.368e+01  1.721e-03   7948.627  < 2e-16 ***
DESTIN_GRID_ID2288          1.128e+01  6.842e-03   1648.048  < 2e-16 ***
DESTIN_GRID_ID2310          1.336e+01  2.212e-03   6040.814  < 2e-16 ***
DESTIN_GRID_ID2312          1.233e+01  5.091e-03   2422.597  < 2e-16 ***
DESTIN_GRID_ID2313          1.450e+01  1.721e-03   8424.514  < 2e-16 ***
DESTIN_GRID_ID2314          1.452e+01  1.588e-03   9146.824  < 2e-16 ***
DESTIN_GRID_ID2315          1.254e+01  2.674e-03   4691.176  < 2e-16 ***
DESTIN_GRID_ID2316          1.323e+01  2.032e-03   6510.627  < 2e-16 ***
DESTIN_GRID_ID2335          1.170e+01  1.356e-02    863.240  < 2e-16 ***
DESTIN_GRID_ID2339          1.338e+01  2.586e-03   5174.072  < 2e-16 ***
DESTIN_GRID_ID2340          1.323e+01  1.936e-03   6835.473  < 2e-16 ***
DESTIN_GRID_ID2341          1.358e+01  1.770e-03   7671.054  < 2e-16 ***
DESTIN_GRID_ID2342          1.240e+01  2.424e-03   5115.875  < 2e-16 ***
DESTIN_GRID_ID2343          1.225e+01  3.844e-03   3186.658  < 2e-16 ***
DESTIN_GRID_ID2363          1.252e+01  3.875e-03   3230.834  < 2e-16 ***
DESTIN_GRID_ID2367          1.303e+01  3.194e-03   4078.983  < 2e-16 ***
DESTIN_GRID_ID2368          1.315e+01  2.280e-03   5768.095  < 2e-16 ***
DESTIN_GRID_ID2369          1.394e+01  1.853e-03   7524.119  < 2e-16 ***
DESTIN_GRID_ID2370          1.481e+01  1.611e-03   9191.422  < 2e-16 ***
DESTIN_GRID_ID2371          1.278e+01  2.624e-03   4871.384  < 2e-16 ***
DESTIN_GRID_ID2390          1.406e+01  1.976e-03   7113.269  < 2e-16 ***
DESTIN_GRID_ID2391          1.384e+01  2.106e-03   6571.018  < 2e-16 ***
DESTIN_GRID_ID2394          1.157e+01  5.931e-03   1950.312  < 2e-16 ***
DESTIN_GRID_ID2395          1.301e+01  2.171e-03   5993.933  < 2e-16 ***
DESTIN_GRID_ID2396          1.309e+01  1.932e-03   6778.992  < 2e-16 ***
DESTIN_GRID_ID2397          1.159e+01  5.587e-03   2073.945  < 2e-16 ***
DESTIN_GRID_ID2398          1.236e+01  3.731e-03   3312.017  < 2e-16 ***
DESTIN_GRID_ID2418          1.330e+01  2.860e-03   4650.068  < 2e-16 ***
DESTIN_GRID_ID2419          1.388e+01  2.382e-03   5826.679  < 2e-16 ***
DESTIN_GRID_ID2422          1.178e+01  9.127e-03   1290.405  < 2e-16 ***
DESTIN_GRID_ID2423          1.218e+01  3.490e-03   3489.177  < 2e-16 ***
DESTIN_GRID_ID2424          1.352e+01  1.905e-03   7094.094  < 2e-16 ***
DESTIN_GRID_ID2425          1.477e+01  1.677e-03   8811.610  < 2e-16 ***
DESTIN_GRID_ID2426          1.290e+01  4.415e-03   2920.607  < 2e-16 ***
DESTIN_GRID_ID2443          1.408e+01  1.967e-03   7155.923  < 2e-16 ***
DESTIN_GRID_ID2445          1.366e+01  2.120e-03   6442.569  < 2e-16 ***
DESTIN_GRID_ID2449          1.202e+01  6.127e-03   1962.331  < 2e-16 ***
DESTIN_GRID_ID2450          1.244e+01  2.748e-03   4528.501  < 2e-16 ***
DESTIN_GRID_ID2451          1.377e+01  1.783e-03   7723.830  < 2e-16 ***
DESTIN_GRID_ID2472          1.114e+01  1.621e-02    687.218  < 2e-16 ***
DESTIN_GRID_ID2473          1.385e+01  2.410e-03   5747.065  < 2e-16 ***
DESTIN_GRID_ID2478          1.268e+01  2.762e-03   4591.579  < 2e-16 ***
DESTIN_GRID_ID2479          1.180e+01  7.754e-03   1522.178  < 2e-16 ***
DESTIN_GRID_ID2497          1.338e+01  2.432e-03   5502.080  < 2e-16 ***
DESTIN_GRID_ID2499          1.272e+01  3.849e-03   3305.561  < 2e-16 ***
DESTIN_GRID_ID2505          1.298e+01  2.931e-03   4427.097  < 2e-16 ***
DESTIN_GRID_ID2527          1.419e+01  1.931e-03   7349.065  < 2e-16 ***
DESTIN_GRID_ID2532          1.204e+01  4.335e-03   2777.644  < 2e-16 ***
DESTIN_GRID_ID2533          1.196e+01  6.452e-03   1853.734  < 2e-16 ***
DESTIN_GRID_ID2551          1.326e+01  3.626e-03   3657.968  < 2e-16 ***
DESTIN_GRID_ID2553          1.253e+01  5.669e-03   2209.991  < 2e-16 ***
DESTIN_GRID_ID2554          1.178e+01  7.150e-03   1647.531  < 2e-16 ***
DESTIN_GRID_ID2559          1.207e+01  5.798e-03   2081.343  < 2e-16 ***
DESTIN_GRID_ID2580          1.355e+01  2.380e-03   5694.418  < 2e-16 ***
DESTIN_GRID_ID2581          1.246e+01  5.042e-03   2470.970  < 2e-16 ***
DESTIN_GRID_ID2607          1.312e+01  2.506e-03   5237.100  < 2e-16 ***
DESTIN_GRID_ID2608          1.213e+01  5.472e-03   2216.545  < 2e-16 ***
DESTIN_GRID_ID2634          1.518e+01  1.633e-03   9291.814  < 2e-16 ***
DESTIN_GRID_ID2635          1.257e+01  3.631e-03   3461.300  < 2e-16 ***
DESTIN_GRID_ID2636          1.342e+01  2.534e-03   5298.092  < 2e-16 ***
DESTIN_GRID_ID2661          1.303e+01  2.336e-03   5577.256  < 2e-16 ***
DESTIN_GRID_ID2663          1.364e+01  1.916e-03   7120.521  < 2e-16 ***
DESTIN_GRID_ID2665          1.405e+01  2.125e-03   6610.449  < 2e-16 ***
DESTIN_GRID_ID2688          1.319e+01  2.618e-03   5039.069  < 2e-16 ***
DESTIN_GRID_ID2689          1.392e+01  2.002e-03   6954.884  < 2e-16 ***
DESTIN_GRID_ID2690          1.353e+01  2.136e-03   6334.669  < 2e-16 ***
DESTIN_GRID_ID2691          1.319e+01  2.143e-03   6154.648  < 2e-16 ***
DESTIN_GRID_ID2693          1.360e+01  2.360e-03   5763.659  < 2e-16 ***
DESTIN_GRID_ID2715          1.310e+01  2.889e-03   4534.976  < 2e-16 ***
DESTIN_GRID_ID2717          1.328e+01  1.925e-03   6896.372  < 2e-16 ***
DESTIN_GRID_ID2718          1.232e+01  3.952e-03   3117.805  < 2e-16 ***
DESTIN_GRID_ID2719          1.345e+01  2.054e-03   6551.301  < 2e-16 ***
DESTIN_GRID_ID2742          1.337e+01  2.510e-03   5327.603  < 2e-16 ***
DESTIN_GRID_ID2743          1.323e+01  3.673e-03   3601.236  < 2e-16 ***
DESTIN_GRID_ID2744          1.380e+01  1.947e-03   7088.478  < 2e-16 ***
DESTIN_GRID_ID2745          1.357e+01  1.959e-03   6927.808  < 2e-16 ***
DESTIN_GRID_ID2747          1.273e+01  3.167e-03   4020.503  < 2e-16 ***
DESTIN_GRID_ID2768          1.339e+01  2.656e-03   5039.639  < 2e-16 ***
DESTIN_GRID_ID2771          1.519e+01  1.599e-03   9503.509  < 2e-16 ***
DESTIN_GRID_ID2773          1.263e+01  2.751e-03   4589.922  < 2e-16 ***
DESTIN_GRID_ID2798          1.193e+01  4.430e-03   2692.408  < 2e-16 ***
DESTIN_GRID_ID2799          1.285e+01  2.341e-03   5489.346  < 2e-16 ***
DESTIN_GRID_ID2800          1.448e+01  1.712e-03   8457.691  < 2e-16 ***
DESTIN_GRID_ID2824          1.426e+01  1.998e-03   7139.241  < 2e-16 ***
DESTIN_GRID_ID2825          1.323e+01  2.000e-03   6612.787  < 2e-16 ***
DESTIN_GRID_ID2826          1.261e+01  3.369e-03   3742.421  < 2e-16 ***
DESTIN_GRID_ID2827          1.506e+01  1.630e-03   9240.185  < 2e-16 ***
DESTIN_GRID_ID2852          1.275e+01  3.247e-03   3927.454  < 2e-16 ***
DESTIN_GRID_ID2853          1.420e+01  1.661e-03   8551.930  < 2e-16 ***
DESTIN_GRID_ID2854          1.358e+01  2.084e-03   6515.249  < 2e-16 ***
DESTIN_GRID_ID2878          1.287e+01  3.169e-03   4062.195  < 2e-16 ***
DESTIN_GRID_ID2879          1.296e+01  2.501e-03   5179.869  < 2e-16 ***
DESTIN_GRID_ID2880          1.239e+01  3.141e-03   3944.581  < 2e-16 ***
DESTIN_GRID_ID2881          1.335e+01  2.724e-03   4900.186  < 2e-16 ***
DESTIN_GRID_ID2907          1.235e+01  4.172e-03   2959.567  < 2e-16 ***
DESTIN_GRID_ID2908          1.364e+01  2.181e-03   6252.640  < 2e-16 ***
DESTIN_GRID_ID2933          1.437e+01  2.757e-03   5211.538  < 2e-16 ***
DESTIN_GRID_ID2934          1.279e+01  3.021e-03   4234.022  < 2e-16 ***
DESTIN_GRID_ID3098          1.385e+01  3.413e-03   4057.014  < 2e-16 ***
log(TORIGIN_BIZ_COUNT)     -6.729e-03  9.835e-05    -68.419  < 2e-16 ***
log(TORIGIN_FINSERV_COUNT)  6.685e-02  8.929e-05    748.698  < 2e-16 ***
log(TORIGIN_MRTEXIT_COUNT)  5.178e-02  1.609e-04    321.881  < 2e-16 ***
log(TORIGIN_BUSSTOP_COUNT)  2.121e-01  2.471e-04    858.370  < 2e-16 ***
log(TORIGIN_HDBCOMM_UNITS) -2.230e-04  5.390e-05     -4.137 3.52e-05 ***
log(TORIGIN_HDBRES_UNITS)   4.342e-01  1.614e-04   2689.853  < 2e-16 ***
log(TORIGIN_SCHOOLS_COUNT)  1.357e-01  2.186e-04    620.853  < 2e-16 ***
log(DISTANCE)              -1.391e+00  1.213e-04 -11467.388  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2954357158  on 101715  degrees of freedom
Residual deviance:  140474768  on 101359  degrees of freedom
AIC: 141233707

Number of Fisher Scoring iterations: 6
CalcRSquared(decSIM_Poisson2$data$TRIPS, decSIM_Poisson2$fitted.values)
[1] 0.5807757
model_list2 <- list(originConstrained2=orcSIM_Poisson2,
                   destinationConstrained2=decSIM_Poisson2,
                   doublyConstrained=dbcSIM_Poisson)
compare_performance(model_list2,
                    metrics = "RMSE")
# Comparison of Model Performance Indices

Name                    | Model |     RMSE
------------------------------------------
originConstrained2      |   glm | 3156.833
destinationConstrained2 |   glm | 3333.398
doublyConstrained       |   glm | 2365.462

8.1.2 Remove outliers

Filter out the 2 extreme trip values: 87864, 71996

inter_zonal_flow1 <- inter_zonal_flow %>%
  filter(TRIPS <71996)

summary(inter_zonal_flow1$TRIPS)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      1      63     300    1790    1295   56944 
orcSIM_Poisson3 <- glm(formula = TRIPS ~ 
                ORIGIN_GRID_ID +
                log(TDESTIN_BIZ_COUNT) +
                log(TDESTIN_FINSERV_COUNT) +
                  log(TDESTIN_MRTEXIT_COUNT) +
                  log(TDESTIN_BUSSTOP_COUNT) +
                  log(TDESTIN_HDBCOMMERCIAL_COUNT) +
                  log(TDESTIN_HDBRESIDENTIAL_COUNT) +
                  log(TDESTIN_HDBCOMM_UNITS) +
                  log(TDESTIN_HDBRES_UNITS) + 
                  log(TDESTIN_SCHOOLS_COUNT) + 
                log(DISTANCE) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow1,
              na.action = na.exclude)
summary(orcSIM_Poisson3)

Call:
glm(formula = TRIPS ~ ORIGIN_GRID_ID + log(TDESTIN_BIZ_COUNT) + 
    log(TDESTIN_FINSERV_COUNT) + log(TDESTIN_MRTEXIT_COUNT) + 
    log(TDESTIN_BUSSTOP_COUNT) + log(TDESTIN_HDBCOMMERCIAL_COUNT) + 
    log(TDESTIN_HDBRESIDENTIAL_COUNT) + log(TDESTIN_HDBCOMM_UNITS) + 
    log(TDESTIN_HDBRES_UNITS) + log(TDESTIN_SCHOOLS_COUNT) + 
    log(DISTANCE) - 1, family = poisson(link = "log"), data = inter_zonal_flow1, 
    na.action = na.exclude)

Coefficients:
                                    Estimate Std. Error   z value Pr(>|z|)    
ORIGIN_GRID_ID664                  1.529e+01  2.328e-02    656.82   <2e-16 ***
ORIGIN_GRID_ID718                  1.927e+01  2.169e-03   8880.66   <2e-16 ***
ORIGIN_GRID_ID745                  1.696e+01  3.088e-03   5490.62   <2e-16 ***
ORIGIN_GRID_ID746                  1.901e+01  2.220e-03   8561.65   <2e-16 ***
ORIGIN_GRID_ID772                  1.869e+01  2.086e-03   8957.97   <2e-16 ***
ORIGIN_GRID_ID799                  1.808e+01  2.810e-03   6434.11   <2e-16 ***
ORIGIN_GRID_ID800                  1.778e+01  2.533e-03   7017.92   <2e-16 ***
ORIGIN_GRID_ID826                  1.892e+01  2.100e-03   9005.69   <2e-16 ***
ORIGIN_GRID_ID827                  1.896e+01  2.281e-03   8311.04   <2e-16 ***
ORIGIN_GRID_ID854                  1.782e+01  2.669e-03   6678.84   <2e-16 ***
ORIGIN_GRID_ID880                  1.724e+01  3.263e-03   5283.79   <2e-16 ***
ORIGIN_GRID_ID881                  1.647e+01  6.231e-03   2643.54   <2e-16 ***
ORIGIN_GRID_ID908                  1.871e+01  2.164e-03   8645.65   <2e-16 ***
ORIGIN_GRID_ID934                  1.738e+01  2.779e-03   6252.54   <2e-16 ***
ORIGIN_GRID_ID935                  1.814e+01  2.352e-03   7709.51   <2e-16 ***
ORIGIN_GRID_ID961                  1.850e+01  2.348e-03   7880.12   <2e-16 ***
ORIGIN_GRID_ID962                  1.872e+01  2.186e-03   8563.19   <2e-16 ***
ORIGIN_GRID_ID987                  1.905e+01  2.195e-03   8680.78   <2e-16 ***
ORIGIN_GRID_ID988                  1.754e+01  2.825e-03   6208.54   <2e-16 ***
ORIGIN_GRID_ID989                  1.865e+01  2.169e-03   8597.13   <2e-16 ***
ORIGIN_GRID_ID1015                 1.745e+01  3.370e-03   5177.73   <2e-16 ***
ORIGIN_GRID_ID1016                 1.764e+01  2.486e-03   7096.00   <2e-16 ***
ORIGIN_GRID_ID1043                 1.786e+01  3.141e-03   5685.25   <2e-16 ***
ORIGIN_GRID_ID1068                 1.552e+01  1.920e-02    808.71   <2e-16 ***
ORIGIN_GRID_ID1070                 1.809e+01  2.342e-03   7724.31   <2e-16 ***
ORIGIN_GRID_ID1096                 1.761e+01  2.403e-03   7329.67   <2e-16 ***
ORIGIN_GRID_ID1097                 1.745e+01  2.988e-03   5840.29   <2e-16 ***
ORIGIN_GRID_ID1099                 1.896e+01  2.149e-03   8821.88   <2e-16 ***
ORIGIN_GRID_ID1122                 1.859e+01  2.268e-03   8197.75   <2e-16 ***
ORIGIN_GRID_ID1123                 1.829e+01  2.249e-03   8129.98   <2e-16 ***
ORIGIN_GRID_ID1124                 1.764e+01  2.619e-03   6734.54   <2e-16 ***
ORIGIN_GRID_ID1125                 1.825e+01  2.488e-03   7335.47   <2e-16 ***
ORIGIN_GRID_ID1127                 1.823e+01  2.176e-03   8379.87   <2e-16 ***
ORIGIN_GRID_ID1128                 1.811e+01  2.464e-03   7350.11   <2e-16 ***
ORIGIN_GRID_ID1148                 1.714e+01  3.230e-03   5306.53   <2e-16 ***
ORIGIN_GRID_ID1150                 1.852e+01  2.147e-03   8626.70   <2e-16 ***
ORIGIN_GRID_ID1151                 1.797e+01  2.366e-03   7594.56   <2e-16 ***
ORIGIN_GRID_ID1152                 1.818e+01  2.667e-03   6817.39   <2e-16 ***
ORIGIN_GRID_ID1153                 1.870e+01  2.237e-03   8361.13   <2e-16 ***
ORIGIN_GRID_ID1154                 1.874e+01  2.206e-03   8494.06   <2e-16 ***
ORIGIN_GRID_ID1155                 1.546e+01  1.048e-02   1476.23   <2e-16 ***
ORIGIN_GRID_ID1176                 1.741e+01  2.869e-03   6070.30   <2e-16 ***
ORIGIN_GRID_ID1178                 1.756e+01  2.447e-03   7175.04   <2e-16 ***
ORIGIN_GRID_ID1179                 1.729e+01  2.736e-03   6320.32   <2e-16 ***
ORIGIN_GRID_ID1180                 1.632e+01  5.684e-03   2871.84   <2e-16 ***
ORIGIN_GRID_ID1181                 1.744e+01  2.328e-03   7493.06   <2e-16 ***
ORIGIN_GRID_ID1182                 1.831e+01  2.174e-03   8423.07   <2e-16 ***
ORIGIN_GRID_ID1183                 1.895e+01  2.724e-03   6956.09   <2e-16 ***
ORIGIN_GRID_ID1205                 1.851e+01  2.168e-03   8535.98   <2e-16 ***
ORIGIN_GRID_ID1206                 1.765e+01  2.575e-03   6854.97   <2e-16 ***
ORIGIN_GRID_ID1207                 1.743e+01  3.066e-03   5686.38   <2e-16 ***
ORIGIN_GRID_ID1209                 1.787e+01  2.478e-03   7212.98   <2e-16 ***
ORIGIN_GRID_ID1232                 1.826e+01  2.240e-03   8148.86   <2e-16 ***
ORIGIN_GRID_ID1233                 1.769e+01  3.147e-03   5620.63   <2e-16 ***
ORIGIN_GRID_ID1235                 1.819e+01  2.463e-03   7386.22   <2e-16 ***
ORIGIN_GRID_ID1255                 1.675e+01  1.075e-02   1558.82   <2e-16 ***
ORIGIN_GRID_ID1258                 1.755e+01  3.324e-03   5279.53   <2e-16 ***
ORIGIN_GRID_ID1259                 1.778e+01  2.484e-03   7156.22   <2e-16 ***
ORIGIN_GRID_ID1261                 1.743e+01  2.576e-03   6767.95   <2e-16 ***
ORIGIN_GRID_ID1262                 1.837e+01  2.281e-03   8054.83   <2e-16 ***
ORIGIN_GRID_ID1283                 1.728e+01  3.086e-03   5600.58   <2e-16 ***
ORIGIN_GRID_ID1284                 1.786e+01  3.203e-03   5576.26   <2e-16 ***
ORIGIN_GRID_ID1286                 1.718e+01  4.038e-03   4255.06   <2e-16 ***
ORIGIN_GRID_ID1289                 1.761e+01  2.406e-03   7317.48   <2e-16 ***
ORIGIN_GRID_ID1309                 1.884e+01  2.402e-03   7842.75   <2e-16 ***
ORIGIN_GRID_ID1310                 1.855e+01  2.248e-03   8250.41   <2e-16 ***
ORIGIN_GRID_ID1315                 1.795e+01  2.332e-03   7696.20   <2e-16 ***
ORIGIN_GRID_ID1316                 1.684e+01  3.545e-03   4750.18   <2e-16 ***
ORIGIN_GRID_ID1337                 1.817e+01  2.349e-03   7732.98   <2e-16 ***
ORIGIN_GRID_ID1338                 1.774e+01  5.451e-03   3254.94   <2e-16 ***
ORIGIN_GRID_ID1343                 1.736e+01  2.628e-03   6604.82   <2e-16 ***
ORIGIN_GRID_ID1363                 1.743e+01  3.590e-03   4854.93   <2e-16 ***
ORIGIN_GRID_ID1364                 1.740e+01  2.842e-03   6121.33   <2e-16 ***
ORIGIN_GRID_ID1366                 1.756e+01  3.187e-03   5509.69   <2e-16 ***
ORIGIN_GRID_ID1369                 1.810e+01  2.243e-03   8068.62   <2e-16 ***
ORIGIN_GRID_ID1370                 1.839e+01  2.382e-03   7719.28   <2e-16 ***
ORIGIN_GRID_ID1374                 1.713e+01  3.229e-03   5304.86   <2e-16 ***
ORIGIN_GRID_ID1375                 1.840e+01  3.592e-03   5122.41   <2e-16 ***
ORIGIN_GRID_ID1391                 1.644e+01  5.068e-03   3243.89   <2e-16 ***
ORIGIN_GRID_ID1392                 1.674e+01  4.201e-03   3984.47   <2e-16 ***
ORIGIN_GRID_ID1396                 1.670e+01  6.142e-03   2719.93   <2e-16 ***
ORIGIN_GRID_ID1397                 1.714e+01  3.202e-03   5351.65   <2e-16 ***
ORIGIN_GRID_ID1401                 1.819e+01  2.463e-03   7385.91   <2e-16 ***
ORIGIN_GRID_ID1402                 1.876e+01  2.141e-03   8765.50   <2e-16 ***
ORIGIN_GRID_ID1423                 1.907e+01  6.146e-03   3102.24   <2e-16 ***
ORIGIN_GRID_ID1428                 1.831e+01  2.412e-03   7591.85   <2e-16 ***
ORIGIN_GRID_ID1429                 1.785e+01  3.514e-03   5078.30   <2e-16 ***
ORIGIN_GRID_ID1455                 1.715e+01  3.057e-03   5610.73   <2e-16 ***
ORIGIN_GRID_ID1456                 1.840e+01  2.235e-03   8233.40   <2e-16 ***
ORIGIN_GRID_ID1471                 1.785e+01  2.584e-03   6909.46   <2e-16 ***
ORIGIN_GRID_ID1482                 1.798e+01  2.347e-03   7658.64   <2e-16 ***
ORIGIN_GRID_ID1499                 1.785e+01  2.555e-03   6988.31   <2e-16 ***
ORIGIN_GRID_ID1509                 1.738e+01  3.741e-03   4645.64   <2e-16 ***
ORIGIN_GRID_ID1510                 1.901e+01  2.081e-03   9133.79   <2e-16 ***
ORIGIN_GRID_ID1525                 1.742e+01  2.738e-03   6362.56   <2e-16 ***
ORIGIN_GRID_ID1536                 1.787e+01  2.281e-03   7834.95   <2e-16 ***
ORIGIN_GRID_ID1537                 1.743e+01  3.896e-03   4473.36   <2e-16 ***
ORIGIN_GRID_ID1552                 1.416e+01  1.434e-02    987.37   <2e-16 ***
ORIGIN_GRID_ID1553                 1.658e+01  3.310e-03   5008.30   <2e-16 ***
ORIGIN_GRID_ID1563                 1.752e+01  3.532e-03   4961.12   <2e-16 ***
ORIGIN_GRID_ID1564                 1.894e+01  2.062e-03   9187.17   <2e-16 ***
ORIGIN_GRID_ID1578                 1.554e+01  7.330e-03   2120.01   <2e-16 ***
ORIGIN_GRID_ID1579                 1.788e+01  2.599e-03   6880.50   <2e-16 ***
ORIGIN_GRID_ID1590                 1.868e+01  2.134e-03   8752.35   <2e-16 ***
ORIGIN_GRID_ID1591                 1.899e+01  2.180e-03   8708.38   <2e-16 ***
ORIGIN_GRID_ID1605                 1.688e+01  3.164e-03   5333.87   <2e-16 ***
ORIGIN_GRID_ID1606                 1.690e+01  3.136e-03   5388.39   <2e-16 ***
ORIGIN_GRID_ID1617                 1.695e+01  5.937e-03   2855.76   <2e-16 ***
ORIGIN_GRID_ID1618                 1.865e+01  2.219e-03   8403.56   <2e-16 ***
ORIGIN_GRID_ID1631                 1.601e+01  5.373e-03   2980.66   <2e-16 ***
ORIGIN_GRID_ID1632                 1.746e+01  2.648e-03   6591.24   <2e-16 ***
ORIGIN_GRID_ID1634                 1.729e+01  4.023e-03   4297.32   <2e-16 ***
ORIGIN_GRID_ID1644                 1.756e+01  2.934e-03   5984.46   <2e-16 ***
ORIGIN_GRID_ID1645                 1.877e+01  2.220e-03   8453.62   <2e-16 ***
ORIGIN_GRID_ID1658                 1.802e+01  2.758e-03   6535.93   <2e-16 ***
ORIGIN_GRID_ID1659                 1.735e+01  2.644e-03   6561.72   <2e-16 ***
ORIGIN_GRID_ID1672                 1.761e+01  3.646e-03   4829.28   <2e-16 ***
ORIGIN_GRID_ID1684                 1.753e+01  2.955e-03   5933.26   <2e-16 ***
ORIGIN_GRID_ID1685                 1.670e+01  3.840e-03   4348.64   <2e-16 ***
ORIGIN_GRID_ID1686                 1.726e+01  2.766e-03   6242.85   <2e-16 ***
ORIGIN_GRID_ID1688                 1.485e+01  1.656e-02    896.95   <2e-16 ***
ORIGIN_GRID_ID1699                 1.704e+01  3.010e-03   5662.36   <2e-16 ***
ORIGIN_GRID_ID1700                 1.487e+01  2.252e-02    660.37   <2e-16 ***
ORIGIN_GRID_ID1712                 1.670e+01  3.884e-03   4300.30   <2e-16 ***
ORIGIN_GRID_ID1713                 1.797e+01  2.329e-03   7716.70   <2e-16 ***
ORIGIN_GRID_ID1727                 1.907e+01  2.112e-03   9032.69   <2e-16 ***
ORIGIN_GRID_ID1739                 1.720e+01  2.685e-03   6406.46   <2e-16 ***
ORIGIN_GRID_ID1753                 1.862e+01  2.206e-03   8441.09   <2e-16 ***
ORIGIN_GRID_ID1754                 1.794e+01  2.998e-03   5984.67   <2e-16 ***
ORIGIN_GRID_ID1766                 1.826e+01  2.296e-03   7952.60   <2e-16 ***
ORIGIN_GRID_ID1767                 1.761e+01  2.316e-03   7604.48   <2e-16 ***
ORIGIN_GRID_ID1780                 1.606e+01  5.977e-03   2687.61   <2e-16 ***
ORIGIN_GRID_ID1781                 1.791e+01  2.350e-03   7620.59   <2e-16 ***
ORIGIN_GRID_ID1792                 1.719e+01  2.957e-03   5813.04   <2e-16 ***
ORIGIN_GRID_ID1793                 1.784e+01  2.290e-03   7788.15   <2e-16 ***
ORIGIN_GRID_ID1794                 1.636e+01  3.934e-03   4159.02   <2e-16 ***
ORIGIN_GRID_ID1807                 1.746e+01  2.558e-03   6825.79   <2e-16 ***
ORIGIN_GRID_ID1820                 1.712e+01  3.046e-03   5619.48   <2e-16 ***
ORIGIN_GRID_ID1821                 1.840e+01  2.196e-03   8378.50   <2e-16 ***
ORIGIN_GRID_ID1833                 1.824e+01  2.120e-03   8602.86   <2e-16 ***
ORIGIN_GRID_ID1835                 1.786e+01  2.788e-03   6408.14   <2e-16 ***
ORIGIN_GRID_ID1847                 1.740e+01  4.115e-03   4229.70   <2e-16 ***
ORIGIN_GRID_ID1854                 1.634e+01  5.860e-03   2788.56   <2e-16 ***
ORIGIN_GRID_ID1859                 1.721e+01  2.334e-03   7372.19   <2e-16 ***
ORIGIN_GRID_ID1860                 1.765e+01  2.280e-03   7741.59   <2e-16 ***
ORIGIN_GRID_ID1861                 1.842e+01  2.447e-03   7525.06   <2e-16 ***
ORIGIN_GRID_ID1874                 1.683e+01  3.263e-03   5156.84   <2e-16 ***
ORIGIN_GRID_ID1875                 1.720e+01  2.539e-03   6772.13   <2e-16 ***
ORIGIN_GRID_ID1882                 1.774e+01  2.523e-03   7029.78   <2e-16 ***
ORIGIN_GRID_ID1883                 1.716e+01  3.638e-03   4715.66   <2e-16 ***
ORIGIN_GRID_ID1886                 1.842e+01  2.210e-03   8330.74   <2e-16 ***
ORIGIN_GRID_ID1887                 1.826e+01  2.156e-03   8472.56   <2e-16 ***
ORIGIN_GRID_ID1888                 1.744e+01  2.949e-03   5912.69   <2e-16 ***
ORIGIN_GRID_ID1905                 1.572e+01  4.867e-03   3229.47   <2e-16 ***
ORIGIN_GRID_ID1907                 1.717e+01  3.018e-03   5687.77   <2e-16 ***
ORIGIN_GRID_ID1908                 1.657e+01  3.781e-03   4382.71   <2e-16 ***
ORIGIN_GRID_ID1909                 1.784e+01  2.397e-03   7443.12   <2e-16 ***
ORIGIN_GRID_ID1912                 1.582e+01  8.652e-03   1828.59   <2e-16 ***
ORIGIN_GRID_ID1913                 1.711e+01  2.640e-03   6479.81   <2e-16 ***
ORIGIN_GRID_ID1914                 1.874e+01  2.127e-03   8810.30   <2e-16 ***
ORIGIN_GRID_ID1928                 1.605e+01  3.367e-03   4765.87   <2e-16 ***
ORIGIN_GRID_ID1929                 1.592e+01  4.393e-03   3624.17   <2e-16 ***
ORIGIN_GRID_ID1933                 1.685e+01  3.302e-03   5101.96   <2e-16 ***
ORIGIN_GRID_ID1935                 1.728e+01  2.952e-03   5853.00   <2e-16 ***
ORIGIN_GRID_ID1936                 1.767e+01  2.558e-03   6909.56   <2e-16 ***
ORIGIN_GRID_ID1937                 1.703e+01  3.176e-03   5361.68   <2e-16 ***
ORIGIN_GRID_ID1940                 1.781e+01  2.626e-03   6780.91   <2e-16 ***
ORIGIN_GRID_ID1941                 1.784e+01  2.379e-03   7500.51   <2e-16 ***
ORIGIN_GRID_ID1942                 1.744e+01  4.488e-03   3885.30   <2e-16 ***
ORIGIN_GRID_ID1955                 1.775e+01  2.539e-03   6988.95   <2e-16 ***
ORIGIN_GRID_ID1959                 1.741e+01  2.462e-03   7071.94   <2e-16 ***
ORIGIN_GRID_ID1960                 1.774e+01  2.388e-03   7426.93   <2e-16 ***
ORIGIN_GRID_ID1962                 1.744e+01  2.588e-03   6738.05   <2e-16 ***
ORIGIN_GRID_ID1963                 1.671e+01  2.779e-03   6013.78   <2e-16 ***
ORIGIN_GRID_ID1967                 1.899e+01  2.129e-03   8923.50   <2e-16 ***
ORIGIN_GRID_ID1968                 1.912e+01  2.220e-03   8614.31   <2e-16 ***
ORIGIN_GRID_ID1985                 1.598e+01  3.576e-03   4469.58   <2e-16 ***
ORIGIN_GRID_ID1987                 1.821e+01  2.200e-03   8276.54   <2e-16 ***
ORIGIN_GRID_ID1988                 1.672e+01  2.927e-03   5713.49   <2e-16 ***
ORIGIN_GRID_ID1989                 1.695e+01  2.964e-03   5716.77   <2e-16 ***
ORIGIN_GRID_ID1990                 1.871e+01  2.152e-03   8694.08   <2e-16 ***
ORIGIN_GRID_ID1994                 1.709e+01  5.479e-03   3118.79   <2e-16 ***
ORIGIN_GRID_ID1995                 1.927e+01  2.139e-03   9007.62   <2e-16 ***
ORIGIN_GRID_ID2010                 1.602e+01  2.926e-03   5474.20   <2e-16 ***
ORIGIN_GRID_ID2011                 1.709e+01  2.356e-03   7252.84   <2e-16 ***
ORIGIN_GRID_ID2012                 1.615e+01  4.112e-03   3926.69   <2e-16 ***
ORIGIN_GRID_ID2013                 1.700e+01  2.653e-03   6409.16   <2e-16 ***
ORIGIN_GRID_ID2014                 1.731e+01  2.482e-03   6973.62   <2e-16 ***
ORIGIN_GRID_ID2015                 1.729e+01  3.166e-03   5462.74   <2e-16 ***
ORIGIN_GRID_ID2016                 1.748e+01  2.504e-03   6980.85   <2e-16 ***
ORIGIN_GRID_ID2017                 1.748e+01  2.527e-03   6917.81   <2e-16 ***
ORIGIN_GRID_ID2021                 1.742e+01  3.717e-03   4684.97   <2e-16 ***
ORIGIN_GRID_ID2038                 1.633e+01  2.435e-03   6707.04   <2e-16 ***
ORIGIN_GRID_ID2039                 1.774e+01  2.729e-03   6500.04   <2e-16 ***
ORIGIN_GRID_ID2040                 1.797e+01  2.299e-03   7813.54   <2e-16 ***
ORIGIN_GRID_ID2041                 1.882e+01  2.170e-03   8670.58   <2e-16 ***
ORIGIN_GRID_ID2042                 1.724e+01  2.910e-03   5925.66   <2e-16 ***
ORIGIN_GRID_ID2043                 1.602e+01  5.185e-03   3088.89   <2e-16 ***
ORIGIN_GRID_ID2044                 1.851e+01  2.173e-03   8517.48   <2e-16 ***
ORIGIN_GRID_ID2064                 1.401e+01  9.050e-03   1548.25   <2e-16 ***
ORIGIN_GRID_ID2065                 1.623e+01  2.909e-03   5578.61   <2e-16 ***
ORIGIN_GRID_ID2066                 1.653e+01  2.904e-03   5690.95   <2e-16 ***
ORIGIN_GRID_ID2067                 1.785e+01  2.634e-03   6777.69   <2e-16 ***
ORIGIN_GRID_ID2068                 1.792e+01  2.598e-03   6896.54   <2e-16 ***
ORIGIN_GRID_ID2070                 1.801e+01  2.725e-03   6607.13   <2e-16 ***
ORIGIN_GRID_ID2071                 1.737e+01  3.316e-03   5239.10   <2e-16 ***
ORIGIN_GRID_ID2093                 1.652e+01  2.540e-03   6504.17   <2e-16 ***
ORIGIN_GRID_ID2094                 1.765e+01  2.759e-03   6396.92   <2e-16 ***
ORIGIN_GRID_ID2095                 1.829e+01  3.096e-03   5908.88   <2e-16 ***
ORIGIN_GRID_ID2098                 1.651e+01  4.381e-03   3768.02   <2e-16 ***
ORIGIN_GRID_ID2119                 1.696e+01  2.848e-03   5953.20   <2e-16 ***
ORIGIN_GRID_ID2120                 1.667e+01  3.099e-03   5377.45   <2e-16 ***
ORIGIN_GRID_ID2123                 1.717e+01  2.682e-03   6402.10   <2e-16 ***
ORIGIN_GRID_ID2147                 1.705e+01  2.542e-03   6708.82   <2e-16 ***
ORIGIN_GRID_ID2148                 1.804e+01  2.274e-03   7934.03   <2e-16 ***
ORIGIN_GRID_ID2149                 1.720e+01  3.159e-03   5444.45   <2e-16 ***
ORIGIN_GRID_ID2150                 1.585e+01  4.419e-03   3585.55   <2e-16 ***
ORIGIN_GRID_ID2151                 1.682e+01  3.038e-03   5537.85   <2e-16 ***
ORIGIN_GRID_ID2152                 1.774e+01  2.787e-03   6367.30   <2e-16 ***
ORIGIN_GRID_ID2154                 1.724e+01  3.362e-03   5128.24   <2e-16 ***
ORIGIN_GRID_ID2174                 1.653e+01  4.076e-03   4055.97   <2e-16 ***
ORIGIN_GRID_ID2177                 1.851e+01  2.159e-03   8572.52   <2e-16 ***
ORIGIN_GRID_ID2178                 1.759e+01  2.346e-03   7499.76   <2e-16 ***
ORIGIN_GRID_ID2179                 1.792e+01  2.533e-03   7077.11   <2e-16 ***
ORIGIN_GRID_ID2180                 1.775e+01  2.948e-03   6020.26   <2e-16 ***
ORIGIN_GRID_ID2201                 1.767e+01  2.454e-03   7198.38   <2e-16 ***
ORIGIN_GRID_ID2203                 1.741e+01  3.573e-03   4871.96   <2e-16 ***
ORIGIN_GRID_ID2204                 1.635e+01  3.631e-03   4504.20   <2e-16 ***
ORIGIN_GRID_ID2205                 1.686e+01  2.523e-03   6682.30   <2e-16 ***
ORIGIN_GRID_ID2206                 1.886e+01  2.111e-03   8931.46   <2e-16 ***
ORIGIN_GRID_ID2208                 1.835e+01  2.500e-03   7337.88   <2e-16 ***
ORIGIN_GRID_ID2228                 1.719e+01  2.648e-03   6493.36   <2e-16 ***
ORIGIN_GRID_ID2231                 1.726e+01  2.496e-03   6913.73   <2e-16 ***
ORIGIN_GRID_ID2233                 1.882e+01  2.100e-03   8963.47   <2e-16 ***
ORIGIN_GRID_ID2234                 1.514e+01  2.498e-02    606.12   <2e-16 ***
ORIGIN_GRID_ID2235                 1.507e+01  2.059e-02    731.97   <2e-16 ***
ORIGIN_GRID_ID2254                 1.605e+01  8.043e-03   1995.58   <2e-16 ***
ORIGIN_GRID_ID2255                 1.747e+01  2.736e-03   6384.26   <2e-16 ***
ORIGIN_GRID_ID2256                 1.711e+01  2.764e-03   6187.66   <2e-16 ***
ORIGIN_GRID_ID2257                 1.585e+01  1.237e-02   1281.54   <2e-16 ***
ORIGIN_GRID_ID2259                 1.608e+01  5.798e-03   2773.91   <2e-16 ***
ORIGIN_GRID_ID2260                 1.833e+01  2.236e-03   8196.32   <2e-16 ***
ORIGIN_GRID_ID2261                 1.853e+01  2.173e-03   8527.24   <2e-16 ***
ORIGIN_GRID_ID2262                 1.750e+01  3.156e-03   5544.43   <2e-16 ***
ORIGIN_GRID_ID2281                 1.739e+01  3.361e-03   5173.38   <2e-16 ***
ORIGIN_GRID_ID2282                 1.694e+01  3.081e-03   5498.89   <2e-16 ***
ORIGIN_GRID_ID2283                 1.759e+01  2.393e-03   7349.48   <2e-16 ***
ORIGIN_GRID_ID2285                 1.825e+01  2.258e-03   8080.78   <2e-16 ***
ORIGIN_GRID_ID2286                 1.697e+01  3.136e-03   5409.73   <2e-16 ***
ORIGIN_GRID_ID2287                 1.882e+01  2.079e-03   9055.02   <2e-16 ***
ORIGIN_GRID_ID2288                 1.659e+01  4.825e-03   3437.91   <2e-16 ***
ORIGIN_GRID_ID2310                 1.711e+01  2.660e-03   6431.81   <2e-16 ***
ORIGIN_GRID_ID2312                 1.524e+01  1.072e-02   1421.69   <2e-16 ***
ORIGIN_GRID_ID2313                 1.756e+01  2.401e-03   7315.74   <2e-16 ***
ORIGIN_GRID_ID2314                 1.803e+01  2.118e-03   8515.68   <2e-16 ***
ORIGIN_GRID_ID2315                 1.740e+01  2.563e-03   6788.84   <2e-16 ***
ORIGIN_GRID_ID2316                 1.858e+01  2.105e-03   8827.42   <2e-16 ***
ORIGIN_GRID_ID2335                 1.516e+01  1.088e-02   1392.99   <2e-16 ***
ORIGIN_GRID_ID2339                 1.743e+01  2.962e-03   5884.16   <2e-16 ***
ORIGIN_GRID_ID2340                 1.822e+01  2.182e-03   8352.36   <2e-16 ***
ORIGIN_GRID_ID2341                 1.787e+01  2.227e-03   8022.90   <2e-16 ***
ORIGIN_GRID_ID2342                 1.729e+01  2.364e-03   7313.33   <2e-16 ***
ORIGIN_GRID_ID2343                 1.742e+01  2.801e-03   6221.06   <2e-16 ***
ORIGIN_GRID_ID2363                 1.684e+01  3.674e-03   4583.56   <2e-16 ***
ORIGIN_GRID_ID2367                 1.729e+01  3.118e-03   5545.73   <2e-16 ***
ORIGIN_GRID_ID2368                 1.801e+01  2.338e-03   7705.69   <2e-16 ***
ORIGIN_GRID_ID2369                 1.762e+01  2.534e-03   6953.59   <2e-16 ***
ORIGIN_GRID_ID2370                 1.805e+01  2.199e-03   8208.97   <2e-16 ***
ORIGIN_GRID_ID2371                 1.815e+01  2.316e-03   7833.90   <2e-16 ***
ORIGIN_GRID_ID2390                 1.703e+01  3.124e-03   5450.12   <2e-16 ***
ORIGIN_GRID_ID2391                 1.703e+01  2.904e-03   5863.10   <2e-16 ***
ORIGIN_GRID_ID2394                 1.646e+01  4.680e-03   3517.86   <2e-16 ***
ORIGIN_GRID_ID2395                 1.850e+01  2.187e-03   8458.95   <2e-16 ***
ORIGIN_GRID_ID2396                 1.808e+01  2.146e-03   8426.02   <2e-16 ***
ORIGIN_GRID_ID2397                 1.726e+01  2.827e-03   6106.09   <2e-16 ***
ORIGIN_GRID_ID2398                 1.761e+01  2.851e-03   6176.20   <2e-16 ***
ORIGIN_GRID_ID2418                 1.709e+01  3.384e-03   5048.84   <2e-16 ***
ORIGIN_GRID_ID2419                 1.641e+01  4.299e-03   3817.32   <2e-16 ***
ORIGIN_GRID_ID2422                 1.699e+01  6.439e-03   2638.61   <2e-16 ***
ORIGIN_GRID_ID2423                 1.738e+01  2.904e-03   5986.82   <2e-16 ***
ORIGIN_GRID_ID2424                 1.839e+01  2.107e-03   8725.73   <2e-16 ***
ORIGIN_GRID_ID2425                 1.785e+01  2.318e-03   7701.68   <2e-16 ***
ORIGIN_GRID_ID2426                 1.718e+01  4.011e-03   4282.66   <2e-16 ***
ORIGIN_GRID_ID2443                 1.765e+01  2.675e-03   6599.42   <2e-16 ***
ORIGIN_GRID_ID2445                 1.786e+01  2.310e-03   7729.99   <2e-16 ***
ORIGIN_GRID_ID2449                 1.804e+01  3.379e-03   5338.48   <2e-16 ***
ORIGIN_GRID_ID2450                 1.789e+01  2.438e-03   7338.18   <2e-16 ***
ORIGIN_GRID_ID2451                 1.837e+01  2.176e-03   8441.80   <2e-16 ***
ORIGIN_GRID_ID2472                 1.565e+01  1.807e-02    866.17   <2e-16 ***
ORIGIN_GRID_ID2473                 1.767e+01  2.754e-03   6415.84   <2e-16 ***
ORIGIN_GRID_ID2478                 1.749e+01  2.606e-03   6712.70   <2e-16 ***
ORIGIN_GRID_ID2479                 1.625e+01  6.093e-03   2667.07   <2e-16 ***
ORIGIN_GRID_ID2497                 1.790e+01  2.459e-03   7277.18   <2e-16 ***
ORIGIN_GRID_ID2499                 1.815e+01  2.711e-03   6695.08   <2e-16 ***
ORIGIN_GRID_ID2505                 1.762e+01  2.722e-03   6474.53   <2e-16 ***
ORIGIN_GRID_ID2527                 1.800e+01  2.455e-03   7331.65   <2e-16 ***
ORIGIN_GRID_ID2532                 1.766e+01  2.927e-03   6033.32   <2e-16 ***
ORIGIN_GRID_ID2533                 1.799e+01  3.378e-03   5324.71   <2e-16 ***
ORIGIN_GRID_ID2551                 1.738e+01  3.273e-03   5309.03   <2e-16 ***
ORIGIN_GRID_ID2553                 1.747e+01  4.380e-03   3988.90   <2e-16 ***
ORIGIN_GRID_ID2554                 1.617e+01  6.478e-03   2496.99   <2e-16 ***
ORIGIN_GRID_ID2559                 1.769e+01  3.279e-03   5394.32   <2e-16 ***
ORIGIN_GRID_ID2580                 1.803e+01  2.505e-03   7197.32   <2e-16 ***
ORIGIN_GRID_ID2581                 1.728e+01  3.956e-03   4367.01   <2e-16 ***
ORIGIN_GRID_ID2607                 1.858e+01  2.208e-03   8416.52   <2e-16 ***
ORIGIN_GRID_ID2608                 1.694e+01  4.181e-03   4052.51   <2e-16 ***
ORIGIN_GRID_ID2634                 1.841e+01  2.339e-03   7871.55   <2e-16 ***
ORIGIN_GRID_ID2635                 1.850e+01  2.508e-03   7377.41   <2e-16 ***
ORIGIN_GRID_ID2636                 1.794e+01  2.685e-03   6679.21   <2e-16 ***
ORIGIN_GRID_ID2661                 1.796e+01  2.363e-03   7598.80   <2e-16 ***
ORIGIN_GRID_ID2663                 1.857e+01  2.106e-03   8819.15   <2e-16 ***
ORIGIN_GRID_ID2665                 1.761e+01  2.961e-03   5947.04   <2e-16 ***
ORIGIN_GRID_ID2688                 1.798e+01  2.437e-03   7379.52   <2e-16 ***
ORIGIN_GRID_ID2689                 1.799e+01  2.507e-03   7178.11   <2e-16 ***
ORIGIN_GRID_ID2690                 1.703e+01  2.922e-03   5828.27   <2e-16 ***
ORIGIN_GRID_ID2691                 1.870e+01  2.140e-03   8739.49   <2e-16 ***
ORIGIN_GRID_ID2693                 1.833e+01  2.289e-03   8005.45   <2e-16 ***
ORIGIN_GRID_ID2715                 1.850e+01  2.436e-03   7594.19   <2e-16 ***
ORIGIN_GRID_ID2717                 1.729e+01  2.371e-03   7291.20   <2e-16 ***
ORIGIN_GRID_ID2718                 1.778e+01  2.872e-03   6189.82   <2e-16 ***
ORIGIN_GRID_ID2719                 1.862e+01  2.080e-03   8949.10   <2e-16 ***
ORIGIN_GRID_ID2742                 1.778e+01  2.795e-03   6361.24   <2e-16 ***
ORIGIN_GRID_ID2743                 1.679e+01  5.284e-03   3177.98   <2e-16 ***
ORIGIN_GRID_ID2744                 1.758e+01  2.429e-03   7239.01   <2e-16 ***
ORIGIN_GRID_ID2745                 1.752e+01  2.328e-03   7525.71   <2e-16 ***
ORIGIN_GRID_ID2747                 1.753e+01  2.718e-03   6449.54   <2e-16 ***
ORIGIN_GRID_ID2768                 1.813e+01  2.666e-03   6798.27   <2e-16 ***
ORIGIN_GRID_ID2771                 1.824e+01  2.181e-03   8365.61   <2e-16 ***
ORIGIN_GRID_ID2773                 1.788e+01  2.364e-03   7563.01   <2e-16 ***
ORIGIN_GRID_ID2798                 1.703e+01  3.228e-03   5274.09   <2e-16 ***
ORIGIN_GRID_ID2799                 1.775e+01  2.239e-03   7928.69   <2e-16 ***
ORIGIN_GRID_ID2800                 1.780e+01  2.412e-03   7380.41   <2e-16 ***
ORIGIN_GRID_ID2824                 1.708e+01  3.176e-03   5376.44   <2e-16 ***
ORIGIN_GRID_ID2825                 1.783e+01  2.187e-03   8149.71   <2e-16 ***
ORIGIN_GRID_ID2826                 1.791e+01  2.625e-03   6821.38   <2e-16 ***
ORIGIN_GRID_ID2827                 1.813e+01  2.315e-03   7833.34   <2e-16 ***
ORIGIN_GRID_ID2852                 1.806e+01  2.393e-03   7547.65   <2e-16 ***
ORIGIN_GRID_ID2853                 1.800e+01  2.145e-03   8393.81   <2e-16 ***
ORIGIN_GRID_ID2854                 1.851e+01  2.154e-03   8595.94   <2e-16 ***
ORIGIN_GRID_ID2878                 1.741e+01  3.104e-03   5610.16   <2e-16 ***
ORIGIN_GRID_ID2879                 1.773e+01  2.457e-03   7216.67   <2e-16 ***
ORIGIN_GRID_ID2880                 1.772e+01  2.441e-03   7259.03   <2e-16 ***
ORIGIN_GRID_ID2881                 1.901e+01  2.190e-03   8681.04   <2e-16 ***
ORIGIN_GRID_ID2907                 1.777e+01  2.743e-03   6476.82   <2e-16 ***
ORIGIN_GRID_ID2908                 1.820e+01  2.395e-03   7599.41   <2e-16 ***
ORIGIN_GRID_ID2933                 1.590e+01  8.024e-03   1982.25   <2e-16 ***
ORIGIN_GRID_ID2934                 1.748e+01  2.882e-03   6065.67   <2e-16 ***
ORIGIN_GRID_ID3098                 1.721e+01  5.578e-03   3086.26   <2e-16 ***
log(TDESTIN_BIZ_COUNT)             3.714e-02  1.032e-04    360.06   <2e-16 ***
log(TDESTIN_FINSERV_COUNT)         2.415e-01  1.043e-04   2314.64   <2e-16 ***
log(TDESTIN_MRTEXIT_COUNT)         6.321e-01  1.524e-04   4146.40   <2e-16 ***
log(TDESTIN_BUSSTOP_COUNT)         1.151e-01  2.510e-04    458.74   <2e-16 ***
log(TDESTIN_HDBCOMMERCIAL_COUNT)   1.316e-01  1.976e-04    666.01   <2e-16 ***
log(TDESTIN_HDBRESIDENTIAL_COUNT)  7.599e-02  4.512e-04    168.44   <2e-16 ***
log(TDESTIN_HDBCOMM_UNITS)         1.924e-03  7.369e-05     26.11   <2e-16 ***
log(TDESTIN_HDBRES_UNITS)         -1.395e-01  3.804e-04   -366.83   <2e-16 ***
log(TDESTIN_SCHOOLS_COUNT)         3.128e-01  2.284e-04   1369.52   <2e-16 ***
log(DISTANCE)                     -1.462e+00  1.270e-04 -11511.35   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2876477793  on 101668  degrees of freedom
Residual deviance:  148889900  on 101310  degrees of freedom
AIC: 149648225

Number of Fisher Scoring iterations: 6
CalcRSquared(orcSIM_Poisson3$data$TRIPS, orcSIM_Poisson3$fitted.values)
[1] 0.6220317
decSIM_Poisson3 <- glm(formula = TRIPS ~ 
                DESTIN_GRID_ID +
                log(TORIGIN_BIZ_COUNT) +
                log(TORIGIN_FINSERV_COUNT) +
                  log(TORIGIN_MRTEXIT_COUNT) +
                  log(TORIGIN_BUSSTOP_COUNT) +
                  log(TORIGIN_HDBCOMMERCIAL_COUNT) +
                  log(TORIGIN_HDBRESIDENTIAL_COUNT) +
                  log(TORIGIN_HDBCOMM_UNITS) +
                  log(TORIGIN_HDBRES_UNITS) + 
                  log(TORIGIN_SCHOOLS_COUNT) + 
                log(DISTANCE) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow1,
              na.action = na.exclude)
summary(decSIM_Poisson3)

Call:
glm(formula = TRIPS ~ DESTIN_GRID_ID + log(TORIGIN_BIZ_COUNT) + 
    log(TORIGIN_FINSERV_COUNT) + log(TORIGIN_MRTEXIT_COUNT) + 
    log(TORIGIN_BUSSTOP_COUNT) + log(TORIGIN_HDBCOMMERCIAL_COUNT) + 
    log(TORIGIN_HDBRESIDENTIAL_COUNT) + log(TORIGIN_HDBCOMM_UNITS) + 
    log(TORIGIN_HDBRES_UNITS) + log(TORIGIN_SCHOOLS_COUNT) + 
    log(DISTANCE) - 1, family = poisson(link = "log"), data = inter_zonal_flow1, 
    na.action = na.exclude)

Coefficients:
                                    Estimate Std. Error   z value Pr(>|z|)    
DESTIN_GRID_ID664                  1.472e+01  4.831e-03   3047.43   <2e-16 ***
DESTIN_GRID_ID718                  1.455e+01  2.483e-03   5860.99   <2e-16 ***
DESTIN_GRID_ID745                  1.296e+01  3.430e-03   3779.63   <2e-16 ***
DESTIN_GRID_ID746                  1.382e+01  2.822e-03   4897.48   <2e-16 ***
DESTIN_GRID_ID772                  1.501e+01  2.205e-03   6805.63   <2e-16 ***
DESTIN_GRID_ID799                  1.507e+01  2.389e-03   6308.49   <2e-16 ***
DESTIN_GRID_ID800                  1.390e+01  2.472e-03   5624.59   <2e-16 ***
DESTIN_GRID_ID826                  1.587e+01  2.211e-03   7178.81   <2e-16 ***
DESTIN_GRID_ID827                  1.478e+01  2.626e-03   5629.81   <2e-16 ***
DESTIN_GRID_ID854                  1.361e+01  3.027e-03   4496.23   <2e-16 ***
DESTIN_GRID_ID880                  1.306e+01  3.924e-03   3329.30   <2e-16 ***
DESTIN_GRID_ID881                  1.361e+01  3.913e-03   3478.30   <2e-16 ***
DESTIN_GRID_ID908                  1.399e+01  2.606e-03   5368.77   <2e-16 ***
DESTIN_GRID_ID934                  1.436e+01  2.543e-03   5646.62   <2e-16 ***
DESTIN_GRID_ID935                  1.403e+01  2.763e-03   5077.72   <2e-16 ***
DESTIN_GRID_ID961                  1.391e+01  2.944e-03   4725.05   <2e-16 ***
DESTIN_GRID_ID962                  1.599e+01  2.190e-03   7303.99   <2e-16 ***
DESTIN_GRID_ID987                  1.498e+01  2.400e-03   6239.43   <2e-16 ***
DESTIN_GRID_ID988                  1.305e+01  3.771e-03   3460.94   <2e-16 ***
DESTIN_GRID_ID989                  1.418e+01  2.624e-03   5403.99   <2e-16 ***
DESTIN_GRID_ID1015                 1.173e+01  8.636e-03   1358.18   <2e-16 ***
DESTIN_GRID_ID1016                 1.333e+01  3.060e-03   4355.04   <2e-16 ***
DESTIN_GRID_ID1043                 1.396e+01  3.439e-03   4058.47   <2e-16 ***
DESTIN_GRID_ID1068                 1.204e+01  2.072e-02    581.44   <2e-16 ***
DESTIN_GRID_ID1070                 1.425e+01  2.512e-03   5674.74   <2e-16 ***
DESTIN_GRID_ID1096                 1.384e+01  2.653e-03   5218.45   <2e-16 ***
DESTIN_GRID_ID1097                 1.346e+01  3.366e-03   3998.17   <2e-16 ***
DESTIN_GRID_ID1099                 1.410e+01  2.603e-03   5418.39   <2e-16 ***
DESTIN_GRID_ID1122                 1.459e+01  2.940e-03   4961.29   <2e-16 ***
DESTIN_GRID_ID1123                 1.557e+01  2.226e-03   6993.82   <2e-16 ***
DESTIN_GRID_ID1124                 1.413e+01  2.640e-03   5352.84   <2e-16 ***
DESTIN_GRID_ID1125                 1.345e+01  3.347e-03   4017.24   <2e-16 ***
DESTIN_GRID_ID1127                 1.363e+01  2.778e-03   4905.41   <2e-16 ***
DESTIN_GRID_ID1128                 1.431e+01  3.116e-03   4591.55   <2e-16 ***
DESTIN_GRID_ID1148                 1.375e+01  3.554e-03   3869.48   <2e-16 ***
DESTIN_GRID_ID1150                 1.418e+01  2.565e-03   5530.11   <2e-16 ***
DESTIN_GRID_ID1151                 1.364e+01  2.811e-03   4851.60   <2e-16 ***
DESTIN_GRID_ID1152                 1.334e+01  3.837e-03   3476.89   <2e-16 ***
DESTIN_GRID_ID1153                 1.401e+01  2.669e-03   5250.36   <2e-16 ***
DESTIN_GRID_ID1154                 1.568e+01  2.198e-03   7132.79   <2e-16 ***
DESTIN_GRID_ID1155                 1.102e+01  1.733e-02    635.80   <2e-16 ***
DESTIN_GRID_ID1176                 1.467e+01  2.573e-03   5701.44   <2e-16 ***
DESTIN_GRID_ID1178                 1.357e+01  2.736e-03   4959.05   <2e-16 ***
DESTIN_GRID_ID1179                 1.279e+01  3.644e-03   3509.86   <2e-16 ***
DESTIN_GRID_ID1180                 1.126e+01  1.032e-02   1090.92   <2e-16 ***
DESTIN_GRID_ID1181                 1.437e+01  2.385e-03   6025.53   <2e-16 ***
DESTIN_GRID_ID1182                 1.389e+01  2.789e-03   4978.66   <2e-16 ***
DESTIN_GRID_ID1183                 1.376e+01  5.276e-03   2609.03   <2e-16 ***
DESTIN_GRID_ID1205                 1.518e+01  2.247e-03   6757.42   <2e-16 ***
DESTIN_GRID_ID1206                 1.398e+01  2.795e-03   5002.40   <2e-16 ***
DESTIN_GRID_ID1207                 1.379e+01  2.949e-03   4676.24   <2e-16 ***
DESTIN_GRID_ID1209                 1.542e+01  2.299e-03   6705.31   <2e-16 ***
DESTIN_GRID_ID1232                 1.440e+01  2.450e-03   5876.24   <2e-16 ***
DESTIN_GRID_ID1233                 1.499e+01  2.681e-03   5591.87   <2e-16 ***
DESTIN_GRID_ID1235                 1.473e+01  2.474e-03   5954.16   <2e-16 ***
DESTIN_GRID_ID1255                 1.478e+01  5.879e-03   2514.72   <2e-16 ***
DESTIN_GRID_ID1258                 1.514e+01  2.560e-03   5914.91   <2e-16 ***
DESTIN_GRID_ID1259                 1.364e+01  3.146e-03   4334.64   <2e-16 ***
DESTIN_GRID_ID1261                 1.351e+01  2.954e-03   4573.93   <2e-16 ***
DESTIN_GRID_ID1262                 1.398e+01  2.660e-03   5258.14   <2e-16 ***
DESTIN_GRID_ID1283                 1.379e+01  3.221e-03   4281.81   <2e-16 ***
DESTIN_GRID_ID1284                 1.336e+01  4.948e-03   2700.72   <2e-16 ***
DESTIN_GRID_ID1286                 1.273e+01  4.822e-03   2639.51   <2e-16 ***
DESTIN_GRID_ID1289                 1.447e+01  2.332e-03   6202.04   <2e-16 ***
DESTIN_GRID_ID1309                 1.497e+01  2.709e-03   5524.41   <2e-16 ***
DESTIN_GRID_ID1310                 1.564e+01  2.287e-03   6839.88   <2e-16 ***
DESTIN_GRID_ID1315                 1.522e+01  2.264e-03   6723.19   <2e-16 ***
DESTIN_GRID_ID1316                 1.298e+01  4.029e-03   3221.47   <2e-16 ***
DESTIN_GRID_ID1337                 1.396e+01  2.726e-03   5120.28   <2e-16 ***
DESTIN_GRID_ID1338                 1.320e+01  6.056e-03   2179.84   <2e-16 ***
DESTIN_GRID_ID1343                 1.299e+01  3.303e-03   3932.48   <2e-16 ***
DESTIN_GRID_ID1363                 1.473e+01  2.972e-03   4954.37   <2e-16 ***
DESTIN_GRID_ID1364                 1.351e+01  3.423e-03   3945.30   <2e-16 ***
DESTIN_GRID_ID1366                 1.391e+01  3.272e-03   4250.67   <2e-16 ***
DESTIN_GRID_ID1369                 1.407e+01  2.672e-03   5264.89   <2e-16 ***
DESTIN_GRID_ID1370                 1.390e+01  2.857e-03   4864.85   <2e-16 ***
DESTIN_GRID_ID1374                 1.326e+01  3.560e-03   3726.22   <2e-16 ***
DESTIN_GRID_ID1375                 1.368e+01  5.840e-03   2343.10   <2e-16 ***
DESTIN_GRID_ID1391                 1.360e+01  4.328e-03   3142.36   <2e-16 ***
DESTIN_GRID_ID1392                 1.247e+01  6.737e-03   1850.66   <2e-16 ***
DESTIN_GRID_ID1396                 1.232e+01  8.428e-03   1462.01   <2e-16 ***
DESTIN_GRID_ID1397                 1.351e+01  3.052e-03   4426.33   <2e-16 ***
DESTIN_GRID_ID1401                 1.509e+01  2.374e-03   6355.58   <2e-16 ***
DESTIN_GRID_ID1402                 1.416e+01  2.611e-03   5423.21   <2e-16 ***
DESTIN_GRID_ID1423                 1.362e+01  4.547e-03   2994.49   <2e-16 ***
DESTIN_GRID_ID1428                 1.357e+01  3.090e-03   4392.77   <2e-16 ***
DESTIN_GRID_ID1429                 1.425e+01  3.292e-03   4327.65   <2e-16 ***
DESTIN_GRID_ID1455                 1.344e+01  3.124e-03   4301.35   <2e-16 ***
DESTIN_GRID_ID1456                 1.371e+01  2.970e-03   4615.69   <2e-16 ***
DESTIN_GRID_ID1471                 1.419e+01  3.396e-03   4178.72   <2e-16 ***
DESTIN_GRID_ID1482                 1.506e+01  2.310e-03   6519.35   <2e-16 ***
DESTIN_GRID_ID1499                 1.336e+01  4.940e-03   2703.39   <2e-16 ***
DESTIN_GRID_ID1509                 1.293e+01  4.963e-03   2605.49   <2e-16 ***
DESTIN_GRID_ID1510                 1.587e+01  2.187e-03   7254.28   <2e-16 ***
DESTIN_GRID_ID1525                 1.473e+01  2.547e-03   5785.09   <2e-16 ***
DESTIN_GRID_ID1536                 1.440e+01  2.369e-03   6078.07   <2e-16 ***
DESTIN_GRID_ID1537                 1.450e+01  3.093e-03   4688.32   <2e-16 ***
DESTIN_GRID_ID1552                 1.219e+01  9.552e-03   1276.39   <2e-16 ***
DESTIN_GRID_ID1553                 1.360e+01  3.582e-03   3795.51   <2e-16 ***
DESTIN_GRID_ID1563                 1.422e+01  2.869e-03   4955.18   <2e-16 ***
DESTIN_GRID_ID1564                 1.424e+01  2.370e-03   6008.41   <2e-16 ***
DESTIN_GRID_ID1578                 1.231e+01  6.535e-03   1883.91   <2e-16 ***
DESTIN_GRID_ID1579                 1.447e+01  2.694e-03   5371.20   <2e-16 ***
DESTIN_GRID_ID1590                 1.396e+01  2.605e-03   5357.13   <2e-16 ***
DESTIN_GRID_ID1591                 1.439e+01  2.595e-03   5544.23   <2e-16 ***
DESTIN_GRID_ID1605                 1.391e+01  2.961e-03   4695.92   <2e-16 ***
DESTIN_GRID_ID1606                 1.387e+01  3.030e-03   4577.17   <2e-16 ***
DESTIN_GRID_ID1617                 1.277e+01  6.707e-03   1903.61   <2e-16 ***
DESTIN_GRID_ID1618                 1.577e+01  2.205e-03   7154.37   <2e-16 ***
DESTIN_GRID_ID1631                 1.352e+01  3.570e-03   3788.09   <2e-16 ***
DESTIN_GRID_ID1632                 1.363e+01  3.120e-03   4369.97   <2e-16 ***
DESTIN_GRID_ID1634                 1.361e+01  4.717e-03   2884.63   <2e-16 ***
DESTIN_GRID_ID1644                 1.403e+01  2.877e-03   4876.45   <2e-16 ***
DESTIN_GRID_ID1645                 1.449e+01  2.536e-03   5713.40   <2e-16 ***
DESTIN_GRID_ID1658                 1.346e+01  3.709e-03   3628.58   <2e-16 ***
DESTIN_GRID_ID1659                 1.419e+01  2.581e-03   5495.86   <2e-16 ***
DESTIN_GRID_ID1672                 1.395e+01  3.839e-03   3634.38   <2e-16 ***
DESTIN_GRID_ID1684                 1.412e+01  2.939e-03   4803.08   <2e-16 ***
DESTIN_GRID_ID1685                 1.382e+01  3.797e-03   3638.67   <2e-16 ***
DESTIN_GRID_ID1686                 1.383e+01  2.959e-03   4674.18   <2e-16 ***
DESTIN_GRID_ID1688                 1.328e+01  6.161e-03   2155.37   <2e-16 ***
DESTIN_GRID_ID1699                 1.413e+01  2.687e-03   5260.06   <2e-16 ***
DESTIN_GRID_ID1700                 1.369e+01  6.195e-03   2210.11   <2e-16 ***
DESTIN_GRID_ID1712                 1.277e+01  4.311e-03   2961.70   <2e-16 ***
DESTIN_GRID_ID1713                 1.458e+01  2.461e-03   5923.28   <2e-16 ***
DESTIN_GRID_ID1727                 1.432e+01  2.533e-03   5653.88   <2e-16 ***
DESTIN_GRID_ID1739                 1.469e+01  2.401e-03   6117.65   <2e-16 ***
DESTIN_GRID_ID1753                 1.566e+01  2.198e-03   7123.72   <2e-16 ***
DESTIN_GRID_ID1754                 1.381e+01  3.143e-03   4392.33   <2e-16 ***
DESTIN_GRID_ID1766                 1.414e+01  2.576e-03   5490.56   <2e-16 ***
DESTIN_GRID_ID1767                 1.413e+01  2.522e-03   5602.26   <2e-16 ***
DESTIN_GRID_ID1780                 1.353e+01  1.017e-02   1331.15   <2e-16 ***
DESTIN_GRID_ID1781                 1.385e+01  2.848e-03   4861.85   <2e-16 ***
DESTIN_GRID_ID1792                 1.323e+01  3.467e-03   3817.09   <2e-16 ***
DESTIN_GRID_ID1793                 1.440e+01  2.454e-03   5867.36   <2e-16 ***
DESTIN_GRID_ID1794                 1.332e+01  3.917e-03   3400.75   <2e-16 ***
DESTIN_GRID_ID1807                 1.263e+01  3.741e-03   3375.77   <2e-16 ***
DESTIN_GRID_ID1820                 1.356e+01  3.226e-03   4204.13   <2e-16 ***
DESTIN_GRID_ID1821                 1.509e+01  2.338e-03   6455.00   <2e-16 ***
DESTIN_GRID_ID1833                 1.460e+01  2.312e-03   6314.96   <2e-16 ***
DESTIN_GRID_ID1835                 1.295e+01  3.930e-03   3293.90   <2e-16 ***
DESTIN_GRID_ID1847                 1.233e+01  9.381e-03   1314.54   <2e-16 ***
DESTIN_GRID_ID1854                 1.367e+01  3.877e-03   3525.18   <2e-16 ***
DESTIN_GRID_ID1859                 1.339e+01  2.653e-03   5045.92   <2e-16 ***
DESTIN_GRID_ID1860                 1.363e+01  2.723e-03   5006.35   <2e-16 ***
DESTIN_GRID_ID1861                 1.338e+01  3.809e-03   3512.36   <2e-16 ***
DESTIN_GRID_ID1874                 1.389e+01  2.931e-03   4739.59   <2e-16 ***
DESTIN_GRID_ID1875                 1.427e+01  2.555e-03   5585.08   <2e-16 ***
DESTIN_GRID_ID1882                 1.449e+01  2.576e-03   5624.51   <2e-16 ***
DESTIN_GRID_ID1883                 1.308e+01  4.104e-03   3186.83   <2e-16 ***
DESTIN_GRID_ID1886                 1.558e+01  2.234e-03   6976.40   <2e-16 ***
DESTIN_GRID_ID1887                 1.573e+01  2.164e-03   7268.95   <2e-16 ***
DESTIN_GRID_ID1888                 1.348e+01  3.801e-03   3547.12   <2e-16 ***
DESTIN_GRID_ID1905                 1.303e+01  4.264e-03   3054.31   <2e-16 ***
DESTIN_GRID_ID1907                 1.393e+01  2.952e-03   4716.81   <2e-16 ***
DESTIN_GRID_ID1908                 1.328e+01  3.601e-03   3689.49   <2e-16 ***
DESTIN_GRID_ID1909                 1.368e+01  2.964e-03   4614.32   <2e-16 ***
DESTIN_GRID_ID1912                 1.051e+01  2.104e-02    499.59   <2e-16 ***
DESTIN_GRID_ID1913                 1.373e+01  2.618e-03   5244.99   <2e-16 ***
DESTIN_GRID_ID1914                 1.440e+01  2.475e-03   5820.96   <2e-16 ***
DESTIN_GRID_ID1928                 1.383e+01  3.397e-03   4071.86   <2e-16 ***
DESTIN_GRID_ID1929                 1.379e+01  3.485e-03   3956.30   <2e-16 ***
DESTIN_GRID_ID1933                 1.460e+01  2.579e-03   5660.84   <2e-16 ***
DESTIN_GRID_ID1935                 1.401e+01  2.922e-03   4795.19   <2e-16 ***
DESTIN_GRID_ID1936                 1.394e+01  2.899e-03   4809.35   <2e-16 ***
DESTIN_GRID_ID1937                 1.387e+01  2.957e-03   4691.79   <2e-16 ***
DESTIN_GRID_ID1940                 1.364e+01  2.782e-03   4902.27   <2e-16 ***
DESTIN_GRID_ID1941                 1.289e+01  3.638e-03   3544.35   <2e-16 ***
DESTIN_GRID_ID1942                 1.394e+01  4.818e-03   2894.41   <2e-16 ***
DESTIN_GRID_ID1955                 1.465e+01  2.630e-03   5569.21   <2e-16 ***
DESTIN_GRID_ID1959                 1.431e+01  2.628e-03   5446.23   <2e-16 ***
DESTIN_GRID_ID1960                 1.460e+01  2.431e-03   6008.00   <2e-16 ***
DESTIN_GRID_ID1962                 1.347e+01  3.055e-03   4409.37   <2e-16 ***
DESTIN_GRID_ID1963                 1.340e+01  2.941e-03   4554.70   <2e-16 ***
DESTIN_GRID_ID1967                 1.408e+01  2.626e-03   5362.26   <2e-16 ***
DESTIN_GRID_ID1968                 1.411e+01  2.975e-03   4741.72   <2e-16 ***
DESTIN_GRID_ID1985                 1.418e+01  3.135e-03   4521.59   <2e-16 ***
DESTIN_GRID_ID1987                 1.534e+01  2.267e-03   6764.02   <2e-16 ***
DESTIN_GRID_ID1988                 1.319e+01  3.188e-03   4137.64   <2e-16 ***
DESTIN_GRID_ID1989                 1.304e+01  3.541e-03   3682.16   <2e-16 ***
DESTIN_GRID_ID1990                 1.560e+01  2.237e-03   6973.61   <2e-16 ***
DESTIN_GRID_ID1994                 1.158e+01  1.258e-02    920.34   <2e-16 ***
DESTIN_GRID_ID1995                 1.356e+01  3.085e-03   4396.66   <2e-16 ***
DESTIN_GRID_ID2010                 1.431e+01  2.503e-03   5716.65   <2e-16 ***
DESTIN_GRID_ID2011                 1.434e+01  2.690e-03   5329.95   <2e-16 ***
DESTIN_GRID_ID2012                 1.353e+01  3.614e-03   3744.35   <2e-16 ***
DESTIN_GRID_ID2013                 1.365e+01  2.691e-03   5072.53   <2e-16 ***
DESTIN_GRID_ID2014                 1.378e+01  2.598e-03   5305.93   <2e-16 ***
DESTIN_GRID_ID2015                 1.417e+01  3.021e-03   4692.51   <2e-16 ***
DESTIN_GRID_ID2016                 1.378e+01  2.764e-03   4984.52   <2e-16 ***
DESTIN_GRID_ID2017                 1.383e+01  2.755e-03   5021.38   <2e-16 ***
DESTIN_GRID_ID2021                 1.225e+01  6.668e-03   1837.60   <2e-16 ***
DESTIN_GRID_ID2038                 1.499e+01  2.360e-03   6352.13   <2e-16 ***
DESTIN_GRID_ID2039                 1.346e+01  3.601e-03   3736.36   <2e-16 ***
DESTIN_GRID_ID2040                 1.368e+01  2.905e-03   4708.02   <2e-16 ***
DESTIN_GRID_ID2041                 1.441e+01  2.483e-03   5803.40   <2e-16 ***
DESTIN_GRID_ID2042                 1.337e+01  3.485e-03   3837.58   <2e-16 ***
DESTIN_GRID_ID2043                 1.418e+01  2.941e-03   4821.51   <2e-16 ***
DESTIN_GRID_ID2044                 1.408e+01  2.576e-03   5464.73   <2e-16 ***
DESTIN_GRID_ID2064                 1.408e+01  3.057e-03   4604.59   <2e-16 ***
DESTIN_GRID_ID2065                 1.387e+01  3.037e-03   4567.84   <2e-16 ***
DESTIN_GRID_ID2066                 1.392e+01  2.606e-03   5342.33   <2e-16 ***
DESTIN_GRID_ID2067                 1.327e+01  3.510e-03   3781.65   <2e-16 ***
DESTIN_GRID_ID2068                 1.371e+01  3.100e-03   4422.86   <2e-16 ***
DESTIN_GRID_ID2070                 1.420e+01  3.038e-03   4672.65   <2e-16 ***
DESTIN_GRID_ID2071                 1.427e+01  2.792e-03   5109.29   <2e-16 ***
DESTIN_GRID_ID2093                 1.426e+01  2.530e-03   5638.00   <2e-16 ***
DESTIN_GRID_ID2094                 1.417e+01  2.696e-03   5255.14   <2e-16 ***
DESTIN_GRID_ID2095                 1.409e+01  3.412e-03   4128.27   <2e-16 ***
DESTIN_GRID_ID2098                 1.393e+01  3.226e-03   4319.28   <2e-16 ***
DESTIN_GRID_ID2119                 1.401e+01  3.009e-03   4654.66   <2e-16 ***
DESTIN_GRID_ID2120                 1.468e+01  2.605e-03   5636.11   <2e-16 ***
DESTIN_GRID_ID2123                 1.308e+01  3.658e-03   3574.89   <2e-16 ***
DESTIN_GRID_ID2147                 1.423e+01  2.637e-03   5394.86   <2e-16 ***
DESTIN_GRID_ID2148                 1.396e+01  2.679e-03   5211.03   <2e-16 ***
DESTIN_GRID_ID2149                 1.447e+01  2.833e-03   5106.35   <2e-16 ***
DESTIN_GRID_ID2150                 1.221e+01  6.178e-03   1975.76   <2e-16 ***
DESTIN_GRID_ID2151                 1.234e+01  5.402e-03   2283.87   <2e-16 ***
DESTIN_GRID_ID2152                 1.473e+01  2.478e-03   5944.55   <2e-16 ***
DESTIN_GRID_ID2154                 1.262e+01  4.902e-03   2573.64   <2e-16 ***
DESTIN_GRID_ID2174                 1.260e+01  5.099e-03   2470.16   <2e-16 ***
DESTIN_GRID_ID2177                 1.589e+01  2.169e-03   7324.09   <2e-16 ***
DESTIN_GRID_ID2178                 1.293e+01  3.206e-03   4031.02   <2e-16 ***
DESTIN_GRID_ID2179                 1.422e+01  2.605e-03   5458.65   <2e-16 ***
DESTIN_GRID_ID2180                 1.325e+01  3.954e-03   3350.38   <2e-16 ***
DESTIN_GRID_ID2201                 1.388e+01  2.915e-03   4762.42   <2e-16 ***
DESTIN_GRID_ID2203                 1.375e+01  3.917e-03   3509.55   <2e-16 ***
DESTIN_GRID_ID2204                 1.407e+01  2.892e-03   4865.98   <2e-16 ***
DESTIN_GRID_ID2205                 1.337e+01  2.840e-03   4710.23   <2e-16 ***
DESTIN_GRID_ID2206                 1.428e+01  2.386e-03   5987.04   <2e-16 ***
DESTIN_GRID_ID2208                 1.375e+01  3.049e-03   4509.41   <2e-16 ***
DESTIN_GRID_ID2228                 1.355e+01  3.133e-03   4325.25   <2e-16 ***
DESTIN_GRID_ID2231                 1.366e+01  2.810e-03   4863.25   <2e-16 ***
DESTIN_GRID_ID2233                 1.422e+01  2.353e-03   6044.54   <2e-16 ***
DESTIN_GRID_ID2234                 8.120e+00  9.131e-02     88.92   <2e-16 ***
DESTIN_GRID_ID2235                 1.126e+01  3.136e-02    359.04   <2e-16 ***
DESTIN_GRID_ID2254                 1.391e+01  5.866e-03   2371.43   <2e-16 ***
DESTIN_GRID_ID2255                 1.326e+01  4.367e-03   3035.37   <2e-16 ***
DESTIN_GRID_ID2256                 1.363e+01  3.016e-03   4520.97   <2e-16 ***
DESTIN_GRID_ID2257                 1.342e+01  7.892e-03   1700.05   <2e-16 ***
DESTIN_GRID_ID2259                 1.288e+01  4.624e-03   2784.95   <2e-16 ***
DESTIN_GRID_ID2260                 1.345e+01  2.727e-03   4931.49   <2e-16 ***
DESTIN_GRID_ID2261                 1.348e+01  2.720e-03   4955.07   <2e-16 ***
DESTIN_GRID_ID2262                 1.250e+01  5.127e-03   2437.69   <2e-16 ***
DESTIN_GRID_ID2281                 1.346e+01  4.255e-03   3162.57   <2e-16 ***
DESTIN_GRID_ID2282                 1.468e+01  2.500e-03   5870.30   <2e-16 ***
DESTIN_GRID_ID2283                 1.343e+01  3.128e-03   4294.96   <2e-16 ***
DESTIN_GRID_ID2285                 1.417e+01  2.657e-03   5332.50   <2e-16 ***
DESTIN_GRID_ID2286                 1.331e+01  3.145e-03   4232.37   <2e-16 ***
DESTIN_GRID_ID2287                 1.425e+01  2.268e-03   6286.35   <2e-16 ***
DESTIN_GRID_ID2288                 1.186e+01  7.006e-03   1692.92   <2e-16 ***
DESTIN_GRID_ID2310                 1.396e+01  2.695e-03   5177.65   <2e-16 ***
DESTIN_GRID_ID2312                 1.292e+01  5.310e-03   2432.45   <2e-16 ***
DESTIN_GRID_ID2313                 1.508e+01  2.282e-03   6608.12   <2e-16 ***
DESTIN_GRID_ID2314                 1.510e+01  2.170e-03   6961.55   <2e-16 ***
DESTIN_GRID_ID2315                 1.312e+01  3.052e-03   4298.66   <2e-16 ***
DESTIN_GRID_ID2316                 1.380e+01  2.532e-03   5450.71   <2e-16 ***
DESTIN_GRID_ID2335                 1.231e+01  1.365e-02    901.92   <2e-16 ***
DESTIN_GRID_ID2339                 1.397e+01  2.998e-03   4661.25   <2e-16 ***
DESTIN_GRID_ID2340                 1.381e+01  2.442e-03   5654.72   <2e-16 ***
DESTIN_GRID_ID2341                 1.415e+01  2.308e-03   6131.98   <2e-16 ***
DESTIN_GRID_ID2342                 1.297e+01  2.849e-03   4553.49   <2e-16 ***
DESTIN_GRID_ID2343                 1.283e+01  4.133e-03   3103.93   <2e-16 ***
DESTIN_GRID_ID2363                 1.312e+01  4.177e-03   3141.18   <2e-16 ***
DESTIN_GRID_ID2367                 1.361e+01  3.525e-03   3860.10   <2e-16 ***
DESTIN_GRID_ID2368                 1.374e+01  2.736e-03   5022.16   <2e-16 ***
DESTIN_GRID_ID2369                 1.452e+01  2.379e-03   6102.76   <2e-16 ***
DESTIN_GRID_ID2370                 1.539e+01  2.202e-03   6988.18   <2e-16 ***
DESTIN_GRID_ID2371                 1.337e+01  3.048e-03   4385.93   <2e-16 ***
DESTIN_GRID_ID2390                 1.466e+01  2.511e-03   5837.60   <2e-16 ***
DESTIN_GRID_ID2391                 1.442e+01  2.593e-03   5563.17   <2e-16 ***
DESTIN_GRID_ID2394                 1.214e+01  6.114e-03   1986.28   <2e-16 ***
DESTIN_GRID_ID2395                 1.358e+01  2.627e-03   5170.07   <2e-16 ***
DESTIN_GRID_ID2396                 1.367e+01  2.444e-03   5594.02   <2e-16 ***
DESTIN_GRID_ID2397                 1.216e+01  5.790e-03   2100.07   <2e-16 ***
DESTIN_GRID_ID2398                 1.294e+01  4.037e-03   3205.04   <2e-16 ***
DESTIN_GRID_ID2418                 1.387e+01  3.229e-03   4297.30   <2e-16 ***
DESTIN_GRID_ID2419                 1.445e+01  2.807e-03   5148.16   <2e-16 ***
DESTIN_GRID_ID2422                 1.235e+01  9.246e-03   1335.70   <2e-16 ***
DESTIN_GRID_ID2423                 1.275e+01  3.797e-03   3357.96   <2e-16 ***
DESTIN_GRID_ID2424                 1.408e+01  2.420e-03   5818.60   <2e-16 ***
DESTIN_GRID_ID2425                 1.535e+01  2.258e-03   6798.88   <2e-16 ***
DESTIN_GRID_ID2426                 1.349e+01  4.694e-03   2874.77   <2e-16 ***
DESTIN_GRID_ID2443                 1.470e+01  2.539e-03   5790.12   <2e-16 ***
DESTIN_GRID_ID2445                 1.424e+01  2.609e-03   5458.31   <2e-16 ***
DESTIN_GRID_ID2449                 1.260e+01  6.310e-03   1996.91   <2e-16 ***
DESTIN_GRID_ID2450                 1.302e+01  3.140e-03   4145.97   <2e-16 ***
DESTIN_GRID_ID2451                 1.434e+01  2.339e-03   6133.34   <2e-16 ***
DESTIN_GRID_ID2472                 1.172e+01  1.628e-02    719.76   <2e-16 ***
DESTIN_GRID_ID2473                 1.443e+01  2.842e-03   5075.29   <2e-16 ***
DESTIN_GRID_ID2478                 1.324e+01  3.139e-03   4217.66   <2e-16 ***
DESTIN_GRID_ID2479                 1.238e+01  7.905e-03   1565.52   <2e-16 ***
DESTIN_GRID_ID2497                 1.398e+01  2.887e-03   4843.55   <2e-16 ***
DESTIN_GRID_ID2499                 1.330e+01  4.130e-03   3220.22   <2e-16 ***
DESTIN_GRID_ID2505                 1.354e+01  3.285e-03   4121.24   <2e-16 ***
DESTIN_GRID_ID2527                 1.477e+01  2.448e-03   6034.69   <2e-16 ***
DESTIN_GRID_ID2532                 1.260e+01  4.585e-03   2748.56   <2e-16 ***
DESTIN_GRID_ID2533                 1.250e+01  6.618e-03   1889.08   <2e-16 ***
DESTIN_GRID_ID2551                 1.388e+01  3.958e-03   3507.90   <2e-16 ***
DESTIN_GRID_ID2553                 1.317e+01  5.893e-03   2234.97   <2e-16 ***
DESTIN_GRID_ID2554                 1.237e+01  7.311e-03   1691.93   <2e-16 ***
DESTIN_GRID_ID2559                 1.263e+01  5.989e-03   2108.18   <2e-16 ***
DESTIN_GRID_ID2580                 1.417e+01  2.857e-03   4959.47   <2e-16 ***
DESTIN_GRID_ID2581                 1.306e+01  5.273e-03   2476.31   <2e-16 ***
DESTIN_GRID_ID2607                 1.374e+01  2.955e-03   4649.47   <2e-16 ***
DESTIN_GRID_ID2608                 1.271e+01  5.679e-03   2238.73   <2e-16 ***
DESTIN_GRID_ID2634                 1.581e+01  2.280e-03   6932.28   <2e-16 ***
DESTIN_GRID_ID2635                 1.320e+01  3.966e-03   3328.62   <2e-16 ***
DESTIN_GRID_ID2636                 1.399e+01  2.931e-03   4772.21   <2e-16 ***
DESTIN_GRID_ID2661                 1.366e+01  2.827e-03   4831.69   <2e-16 ***
DESTIN_GRID_ID2663                 1.421e+01  2.409e-03   5897.57   <2e-16 ***
DESTIN_GRID_ID2665                 1.458e+01  2.547e-03   5724.91   <2e-16 ***
DESTIN_GRID_ID2688                 1.381e+01  3.051e-03   4526.77   <2e-16 ***
DESTIN_GRID_ID2689                 1.452e+01  2.521e-03   5761.77   <2e-16 ***
DESTIN_GRID_ID2690                 1.410e+01  2.598e-03   5427.52   <2e-16 ***
DESTIN_GRID_ID2691                 1.376e+01  2.597e-03   5296.41   <2e-16 ***
DESTIN_GRID_ID2693                 1.412e+01  2.733e-03   5165.17   <2e-16 ***
DESTIN_GRID_ID2715                 1.373e+01  3.293e-03   4167.64   <2e-16 ***
DESTIN_GRID_ID2717                 1.385e+01  2.430e-03   5700.31   <2e-16 ***
DESTIN_GRID_ID2718                 1.288e+01  4.212e-03   3058.27   <2e-16 ***
DESTIN_GRID_ID2719                 1.397e+01  2.469e-03   5656.87   <2e-16 ***
DESTIN_GRID_ID2742                 1.398e+01  2.947e-03   4742.50   <2e-16 ***
DESTIN_GRID_ID2743                 1.384e+01  3.989e-03   3468.90   <2e-16 ***
DESTIN_GRID_ID2744                 1.437e+01  2.444e-03   5877.46   <2e-16 ***
DESTIN_GRID_ID2745                 1.413e+01  2.440e-03   5792.46   <2e-16 ***
DESTIN_GRID_ID2747                 1.325e+01  3.455e-03   3835.31   <2e-16 ***
DESTIN_GRID_ID2768                 1.400e+01  3.092e-03   4529.38   <2e-16 ***
DESTIN_GRID_ID2771                 1.576e+01  2.163e-03   7285.37   <2e-16 ***
DESTIN_GRID_ID2773                 1.315e+01  3.083e-03   4265.89   <2e-16 ***
DESTIN_GRID_ID2798                 1.250e+01  4.668e-03   2677.38   <2e-16 ***
DESTIN_GRID_ID2799                 1.341e+01  2.747e-03   4880.08   <2e-16 ***
DESTIN_GRID_ID2800                 1.501e+01  2.201e-03   6820.98   <2e-16 ***
DESTIN_GRID_ID2824                 1.482e+01  2.476e-03   5985.30   <2e-16 ***
DESTIN_GRID_ID2825                 1.378e+01  2.468e-03   5583.94   <2e-16 ***
DESTIN_GRID_ID2826                 1.317e+01  3.662e-03   3595.12   <2e-16 ***
DESTIN_GRID_ID2827                 1.559e+01  2.151e-03   7250.25   <2e-16 ***
DESTIN_GRID_ID2852                 1.331e+01  3.559e-03   3738.85   <2e-16 ***
DESTIN_GRID_ID2853                 1.476e+01  2.195e-03   6725.25   <2e-16 ***
DESTIN_GRID_ID2854                 1.410e+01  2.507e-03   5623.08   <2e-16 ***
DESTIN_GRID_ID2878                 1.343e+01  3.494e-03   3844.78   <2e-16 ***
DESTIN_GRID_ID2879                 1.354e+01  2.906e-03   4657.30   <2e-16 ***
DESTIN_GRID_ID2880                 1.293e+01  3.445e-03   3753.47   <2e-16 ***
DESTIN_GRID_ID2881                 1.387e+01  3.063e-03   4528.72   <2e-16 ***
DESTIN_GRID_ID2907                 1.290e+01  4.410e-03   2924.31   <2e-16 ***
DESTIN_GRID_ID2908                 1.417e+01  2.593e-03   5464.74   <2e-16 ***
DESTIN_GRID_ID2933                 1.492e+01  3.116e-03   4788.55   <2e-16 ***
DESTIN_GRID_ID2934                 1.332e+01  3.334e-03   3996.79   <2e-16 ***
DESTIN_GRID_ID3098                 1.438e+01  3.706e-03   3880.32   <2e-16 ***
log(TORIGIN_BIZ_COUNT)             1.206e-03  9.953e-05     12.12   <2e-16 ***
log(TORIGIN_FINSERV_COUNT)         7.748e-02  9.587e-05    808.23   <2e-16 ***
log(TORIGIN_MRTEXIT_COUNT)         5.136e-02  1.625e-04    316.01   <2e-16 ***
log(TORIGIN_BUSSTOP_COUNT)         2.086e-01  2.505e-04    832.58   <2e-16 ***
log(TORIGIN_HDBCOMMERCIAL_COUNT)  -3.287e-02  1.915e-04   -171.67   <2e-16 ***
log(TORIGIN_HDBRESIDENTIAL_COUNT)  1.956e-01  4.300e-04    454.86   <2e-16 ***
log(TORIGIN_HDBCOMM_UNITS)         1.508e-03  7.013e-05     21.50   <2e-16 ***
log(TORIGIN_HDBRES_UNITS)          2.734e-01  3.809e-04    717.92   <2e-16 ***
log(TORIGIN_SCHOOLS_COUNT)         1.248e-01  2.222e-04    561.90   <2e-16 ***
log(DISTANCE)                     -1.379e+00  1.216e-04 -11336.97   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2876477793  on 101668  degrees of freedom
Residual deviance:  138233568  on 101310  degrees of freedom
AIC: 138991893

Number of Fisher Scoring iterations: 6
CalcRSquared(decSIM_Poisson3$data$TRIPS, decSIM_Poisson3$fitted.values)
[1] 0.5688128
dbcSIM_Poisson2 <- glm(formula = TRIPS ~ 
                ORIGIN_GRID_ID + 
                DESTIN_GRID_ID +
                log(DISTANCE),
              family = poisson(link = "log"),
              data = inter_zonal_flow1,
              na.action = na.exclude)
summary(dbcSIM_Poisson2)

Call:
glm(formula = TRIPS ~ ORIGIN_GRID_ID + DESTIN_GRID_ID + log(DISTANCE), 
    family = poisson(link = "log"), data = inter_zonal_flow1, 
    na.action = na.exclude)

Coefficients:
                     Estimate Std. Error    z value Pr(>|z|)    
(Intercept)        16.0149770  0.0236172    678.108  < 2e-16 ***
ORIGIN_GRID_ID718   4.2374331  0.0232019    182.633  < 2e-16 ***
ORIGIN_GRID_ID745   1.7177165  0.0233092     73.693  < 2e-16 ***
ORIGIN_GRID_ID746   3.7772233  0.0232067    162.765  < 2e-16 ***
ORIGIN_GRID_ID772   3.1528957  0.0232007    135.896  < 2e-16 ***
ORIGIN_GRID_ID799   2.5680980  0.0232738    110.343  < 2e-16 ***
ORIGIN_GRID_ID800   2.7238777  0.0232406    117.203  < 2e-16 ***
ORIGIN_GRID_ID826   3.8631518  0.0231983    166.528  < 2e-16 ***
ORIGIN_GRID_ID827   3.7030748  0.0232157    159.507  < 2e-16 ***
ORIGIN_GRID_ID854   2.5137965  0.0232560    108.092  < 2e-16 ***
ORIGIN_GRID_ID880   1.7505642  0.0233329     75.026  < 2e-16 ***
ORIGIN_GRID_ID881   1.1233549  0.0239383     46.927  < 2e-16 ***
ORIGIN_GRID_ID908   3.4343339  0.0232101    147.967  < 2e-16 ***
ORIGIN_GRID_ID934   2.0601753  0.0232816     88.490  < 2e-16 ***
ORIGIN_GRID_ID935   2.7622437  0.0232318    118.899  < 2e-16 ***
ORIGIN_GRID_ID961   3.1093858  0.0232333    133.833  < 2e-16 ***
ORIGIN_GRID_ID962   3.8046508  0.0232199    163.853  < 2e-16 ***
ORIGIN_GRID_ID987   3.9418662  0.0232158    169.792  < 2e-16 ***
ORIGIN_GRID_ID988   2.1007647  0.0232868     90.213  < 2e-16 ***
ORIGIN_GRID_ID989   3.3059440  0.0232161    142.399  < 2e-16 ***
ORIGIN_GRID_ID1015  2.0448177  0.0233612     87.531  < 2e-16 ***
ORIGIN_GRID_ID1016  2.1963105  0.0232495     94.467  < 2e-16 ***
ORIGIN_GRID_ID1043  2.7269032  0.0233235    116.917  < 2e-16 ***
ORIGIN_GRID_ID1068  0.0127083  0.0300513      0.423 0.672379    
ORIGIN_GRID_ID1070  3.0459129  0.0232317    131.110  < 2e-16 ***
ORIGIN_GRID_ID1096  2.5449724  0.0232415    109.501  < 2e-16 ***
ORIGIN_GRID_ID1097  2.5172001  0.0233135    107.972  < 2e-16 ***
ORIGIN_GRID_ID1099  4.5304786  0.0232346    194.988  < 2e-16 ***
ORIGIN_GRID_ID1122  3.4070331  0.0232338    146.641  < 2e-16 ***
ORIGIN_GRID_ID1123  3.0791971  0.0232237    132.588  < 2e-16 ***
ORIGIN_GRID_ID1124  2.6985473  0.0232658    115.988  < 2e-16 ***
ORIGIN_GRID_ID1125  3.3782856  0.0232584    145.250  < 2e-16 ***
ORIGIN_GRID_ID1127  3.6355877  0.0232456    156.399  < 2e-16 ***
ORIGIN_GRID_ID1128  3.3738345  0.0232811    144.917  < 2e-16 ***
ORIGIN_GRID_ID1148  1.7808549  0.0233494     76.270  < 2e-16 ***
ORIGIN_GRID_ID1150  3.5036394  0.0232182    150.900  < 2e-16 ***
ORIGIN_GRID_ID1151  2.9293391  0.0232440    126.026  < 2e-16 ***
ORIGIN_GRID_ID1152  3.3337253  0.0232749    143.232  < 2e-16 ***
ORIGIN_GRID_ID1153  4.1850194  0.0232528    179.979  < 2e-16 ***
ORIGIN_GRID_ID1154  4.0324047  0.0232408    173.505  < 2e-16 ***
ORIGIN_GRID_ID1155  0.8329148  0.0254096     32.780  < 2e-16 ***
ORIGIN_GRID_ID1176  2.2023789  0.0232945     94.545  < 2e-16 ***
ORIGIN_GRID_ID1178  2.4134450  0.0232508    103.801  < 2e-16 ***
ORIGIN_GRID_ID1179  2.2272609  0.0232894     95.634  < 2e-16 ***
ORIGIN_GRID_ID1180  1.5178406  0.0238108     63.746  < 2e-16 ***
ORIGIN_GRID_ID1181  2.8077037  0.0232575    120.722  < 2e-16 ***
ORIGIN_GRID_ID1182  3.2430838  0.0232526    139.472  < 2e-16 ***
ORIGIN_GRID_ID1183  3.6419620  0.0233135    156.217  < 2e-16 ***
ORIGIN_GRID_ID1205  3.6531715  0.0232254    157.292  < 2e-16 ***
ORIGIN_GRID_ID1206  2.7633210  0.0232710    118.745  < 2e-16 ***
ORIGIN_GRID_ID1207  2.6669612  0.0233298    114.316  < 2e-16 ***
ORIGIN_GRID_ID1209  3.3799559  0.0232803    145.185  < 2e-16 ***
ORIGIN_GRID_ID1232  3.0251973  0.0232307    130.224  < 2e-16 ***
ORIGIN_GRID_ID1233  2.5940501  0.0233486    111.101  < 2e-16 ***
ORIGIN_GRID_ID1235  3.5529756  0.0232691    152.691  < 2e-16 ***
ORIGIN_GRID_ID1255  1.6828152  0.0254913     66.015  < 2e-16 ***
ORIGIN_GRID_ID1258  2.3942081  0.0233555    102.511  < 2e-16 ***
ORIGIN_GRID_ID1259  2.6965333  0.0232589    115.936  < 2e-16 ***
ORIGIN_GRID_ID1261  2.6107930  0.0232720    112.186  < 2e-16 ***
ORIGIN_GRID_ID1262  3.5474568  0.0232442    152.617  < 2e-16 ***
ORIGIN_GRID_ID1283  1.8093147  0.0233245     77.572  < 2e-16 ***
ORIGIN_GRID_ID1284  2.2200647  0.0233432     95.105  < 2e-16 ***
ORIGIN_GRID_ID1286  2.0193336  0.0234700     86.039  < 2e-16 ***
ORIGIN_GRID_ID1289  2.6865051  0.0232595    115.502  < 2e-16 ***
ORIGIN_GRID_ID1309  3.5925055  0.0232435    154.560  < 2e-16 ***
ORIGIN_GRID_ID1310  3.6110537  0.0232299    155.449  < 2e-16 ***
ORIGIN_GRID_ID1315  3.1251367  0.0232466    134.434  < 2e-16 ***
ORIGIN_GRID_ID1316  2.0120160  0.0234120     85.939  < 2e-16 ***
ORIGIN_GRID_ID1337  2.4961055  0.0232409    107.401  < 2e-16 ***
ORIGIN_GRID_ID1338  2.1845365  0.0237567     91.954  < 2e-16 ***
ORIGIN_GRID_ID1343  2.5068606  0.0232860    107.655  < 2e-16 ***
ORIGIN_GRID_ID1363  2.0465761  0.0233969     87.472  < 2e-16 ***
ORIGIN_GRID_ID1364  1.9038327  0.0232970     81.720  < 2e-16 ***
ORIGIN_GRID_ID1366  2.5300134  0.0233325    108.433  < 2e-16 ***
ORIGIN_GRID_ID1369  3.2543288  0.0232437    140.009  < 2e-16 ***
ORIGIN_GRID_ID1370  3.7683442  0.0232648    161.976  < 2e-16 ***
ORIGIN_GRID_ID1374  1.6501740  0.0233944     70.537  < 2e-16 ***
ORIGIN_GRID_ID1375  3.0981802  0.0234482    132.129  < 2e-16 ***
ORIGIN_GRID_ID1391  1.0259293  0.0236701     43.343  < 2e-16 ***
ORIGIN_GRID_ID1392  1.6400193  0.0234996     69.789  < 2e-16 ***
ORIGIN_GRID_ID1396  1.7948883  0.0239491     74.946  < 2e-16 ***
ORIGIN_GRID_ID1397  2.3217951  0.0233672     99.361  < 2e-16 ***
ORIGIN_GRID_ID1401  3.1377140  0.0233003    134.664  < 2e-16 ***
ORIGIN_GRID_ID1402  3.4013733  0.0232696    146.172  < 2e-16 ***
ORIGIN_GRID_ID1423  4.2393603  0.0239261    177.186  < 2e-16 ***
ORIGIN_GRID_ID1428  2.7242626  0.0232945    116.949  < 2e-16 ***
ORIGIN_GRID_ID1429  2.2489925  0.0234321     95.979  < 2e-16 ***
ORIGIN_GRID_ID1455  1.5069586  0.0233766     64.464  < 2e-16 ***
ORIGIN_GRID_ID1456  2.6558669  0.0232795    114.086  < 2e-16 ***
ORIGIN_GRID_ID1471  2.8108350  0.0232836    120.722  < 2e-16 ***
ORIGIN_GRID_ID1482  2.2999453  0.0232891     98.756  < 2e-16 ***
ORIGIN_GRID_ID1499  2.8701723  0.0232898    123.237  < 2e-16 ***
ORIGIN_GRID_ID1509  1.9422356  0.0234691     82.757  < 2e-16 ***
ORIGIN_GRID_ID1510  3.7770459  0.0232583    162.396  < 2e-16 ***
ORIGIN_GRID_ID1525  2.5292377  0.0232898    108.599  < 2e-16 ***
ORIGIN_GRID_ID1536  2.4443707  0.0232805    104.996  < 2e-16 ***
ORIGIN_GRID_ID1537  1.5143837  0.0234955     64.454  < 2e-16 ***
ORIGIN_GRID_ID1552 -0.7937246  0.0272336    -29.145  < 2e-16 ***
ORIGIN_GRID_ID1553  1.4529853  0.0233790     62.149  < 2e-16 ***
ORIGIN_GRID_ID1563  2.1306411  0.0234369     90.910  < 2e-16 ***
ORIGIN_GRID_ID1564  3.1751937  0.0232587    136.516  < 2e-16 ***
ORIGIN_GRID_ID1578  0.3956795  0.0242677     16.305  < 2e-16 ***
ORIGIN_GRID_ID1579  2.9757387  0.0232761    127.845  < 2e-16 ***
ORIGIN_GRID_ID1590  3.2476702  0.0232652    139.594  < 2e-16 ***
ORIGIN_GRID_ID1591  3.2713360  0.0232692    140.587  < 2e-16 ***
ORIGIN_GRID_ID1605  1.7237286  0.0233498     73.822  < 2e-16 ***
ORIGIN_GRID_ID1606  1.5239502  0.0233515     65.261  < 2e-16 ***
ORIGIN_GRID_ID1617  1.6689658  0.0239212     69.769  < 2e-16 ***
ORIGIN_GRID_ID1618  3.2077108  0.0232703    137.846  < 2e-16 ***
ORIGIN_GRID_ID1631  0.6641488  0.0237522     27.962  < 2e-16 ***
ORIGIN_GRID_ID1632  2.0533925  0.0232881     88.174  < 2e-16 ***
ORIGIN_GRID_ID1634  2.3635486  0.0234766    100.677  < 2e-16 ***
ORIGIN_GRID_ID1644  2.1341272  0.0233494     91.400  < 2e-16 ***
ORIGIN_GRID_ID1645  3.1106927  0.0232706    133.675  < 2e-16 ***
ORIGIN_GRID_ID1658  2.3146303  0.0233092     99.301  < 2e-16 ***
ORIGIN_GRID_ID1659  2.0424339  0.0232862     87.710  < 2e-16 ***
ORIGIN_GRID_ID1672  1.7852110  0.0234545     76.114  < 2e-16 ***
ORIGIN_GRID_ID1684  2.2383183  0.0233248     95.963  < 2e-16 ***
ORIGIN_GRID_ID1685  1.1533235  0.0234531     49.176  < 2e-16 ***
ORIGIN_GRID_ID1686  2.0762219  0.0233013     89.103  < 2e-16 ***
ORIGIN_GRID_ID1688 -0.2714157  0.0284494     -9.540  < 2e-16 ***
ORIGIN_GRID_ID1699  1.5754556  0.0233565     67.453  < 2e-16 ***
ORIGIN_GRID_ID1700 -0.6301176  0.0323018    -19.507  < 2e-16 ***
ORIGIN_GRID_ID1712  1.1407227  0.0234617     48.621  < 2e-16 ***
ORIGIN_GRID_ID1713  2.5334514  0.0232520    108.956  < 2e-16 ***
ORIGIN_GRID_ID1727  3.7062865  0.0232631    159.320  < 2e-16 ***
ORIGIN_GRID_ID1739  1.6988626  0.0232910     72.941  < 2e-16 ***
ORIGIN_GRID_ID1753  3.2504562  0.0232713    139.677  < 2e-16 ***
ORIGIN_GRID_ID1754  2.6075455  0.0233549    111.649  < 2e-16 ***
ORIGIN_GRID_ID1766  2.5804690  0.0232529    110.974  < 2e-16 ***
ORIGIN_GRID_ID1767  2.1395028  0.0232521     92.013  < 2e-16 ***
ORIGIN_GRID_ID1780  0.7608302  0.0239269     31.798  < 2e-16 ***
ORIGIN_GRID_ID1781  2.5968141  0.0232856    111.520  < 2e-16 ***
ORIGIN_GRID_ID1792  1.6842509  0.0233269     72.202  < 2e-16 ***
ORIGIN_GRID_ID1793  2.2113515  0.0232524     95.102  < 2e-16 ***
ORIGIN_GRID_ID1794  0.9099700  0.0234665     38.777  < 2e-16 ***
ORIGIN_GRID_ID1807  2.1569039  0.0233043     92.554  < 2e-16 ***
ORIGIN_GRID_ID1820  1.7129476  0.0233359     73.404  < 2e-16 ***
ORIGIN_GRID_ID1821  3.0787757  0.0232443    132.453  < 2e-16 ***
ORIGIN_GRID_ID1833  3.0769102  0.0232592    132.288  < 2e-16 ***
ORIGIN_GRID_ID1835  2.6942829  0.0233304    115.484  < 2e-16 ***
ORIGIN_GRID_ID1847  1.4678131  0.0235090     62.436  < 2e-16 ***
ORIGIN_GRID_ID1854  1.3307813  0.0238716     55.747  < 2e-16 ***
ORIGIN_GRID_ID1859  1.9823643  0.0232830     85.142  < 2e-16 ***
ORIGIN_GRID_ID1860  2.4625041  0.0232759    105.796  < 2e-16 ***
ORIGIN_GRID_ID1861  3.2960872  0.0232893    141.528  < 2e-16 ***
ORIGIN_GRID_ID1874  1.5642303  0.0233613     66.958  < 2e-16 ***
ORIGIN_GRID_ID1875  1.6484592  0.0232756     70.823  < 2e-16 ***
ORIGIN_GRID_ID1882  2.7301688  0.0232820    117.265  < 2e-16 ***
ORIGIN_GRID_ID1883  2.1518690  0.0234269     91.855  < 2e-16 ***
ORIGIN_GRID_ID1886  3.3953799  0.0232625    145.960  < 2e-16 ***
ORIGIN_GRID_ID1887  3.1968976  0.0232604    137.440  < 2e-16 ***
ORIGIN_GRID_ID1888  2.3046974  0.0233489     98.707  < 2e-16 ***
ORIGIN_GRID_ID1905  0.6335917  0.0236412     26.800  < 2e-16 ***
ORIGIN_GRID_ID1907  2.2039440  0.0233389     94.432  < 2e-16 ***
ORIGIN_GRID_ID1908  1.4942335  0.0234535     63.711  < 2e-16 ***
ORIGIN_GRID_ID1909  2.8658502  0.0232692    123.161  < 2e-16 ***
ORIGIN_GRID_ID1912  0.6256185  0.0247297     25.298  < 2e-16 ***
ORIGIN_GRID_ID1913  1.9434207  0.0233136     83.360  < 2e-16 ***
ORIGIN_GRID_ID1914  3.5955621  0.0232614    154.572  < 2e-16 ***
ORIGIN_GRID_ID1928  1.2061096  0.0233833     51.580  < 2e-16 ***
ORIGIN_GRID_ID1929  1.0510832  0.0235492     44.633  < 2e-16 ***
ORIGIN_GRID_ID1933  1.7634726  0.0233810     75.423  < 2e-16 ***
ORIGIN_GRID_ID1935  2.1105697  0.0233362     90.442  < 2e-16 ***
ORIGIN_GRID_ID1936  2.5310444  0.0232854    108.697  < 2e-16 ***
ORIGIN_GRID_ID1937  1.9722949  0.0233603     84.429  < 2e-16 ***
ORIGIN_GRID_ID1940  2.8865266  0.0233138    123.812  < 2e-16 ***
ORIGIN_GRID_ID1941  2.7504713  0.0232870    118.112  < 2e-16 ***
ORIGIN_GRID_ID1942  2.3448579  0.0235959     99.376  < 2e-16 ***
ORIGIN_GRID_ID1955  2.5597525  0.0232727    109.990  < 2e-16 ***
ORIGIN_GRID_ID1959  2.3744610  0.0232708    102.036  < 2e-16 ***
ORIGIN_GRID_ID1960  2.5826144  0.0232680    110.994  < 2e-16 ***
ORIGIN_GRID_ID1962  2.2577861  0.0232883     96.949  < 2e-16 ***
ORIGIN_GRID_ID1963  1.4401387  0.0233116     61.778  < 2e-16 ***
ORIGIN_GRID_ID1967  4.0289748  0.0232606    173.210  < 2e-16 ***
ORIGIN_GRID_ID1968  4.0580434  0.0232705    174.386  < 2e-16 ***
ORIGIN_GRID_ID1985  1.3436385  0.0234150     57.384  < 2e-16 ***
ORIGIN_GRID_ID1987  2.9585972  0.0232463    127.272  < 2e-16 ***
ORIGIN_GRID_ID1988  1.5899480  0.0233276     68.157  < 2e-16 ***
ORIGIN_GRID_ID1989  1.8481892  0.0233354     79.201  < 2e-16 ***
ORIGIN_GRID_ID1990  3.7967948  0.0232400    163.373  < 2e-16 ***
ORIGIN_GRID_ID1994  2.1436243  0.0238029     90.057  < 2e-16 ***
ORIGIN_GRID_ID1995  4.3014199  0.0232622    184.911  < 2e-16 ***
ORIGIN_GRID_ID2010  1.3529934  0.0233256     58.005  < 2e-16 ***
ORIGIN_GRID_ID2011  2.2989564  0.0232611     98.833  < 2e-16 ***
ORIGIN_GRID_ID2012  1.1903965  0.0235038     50.647  < 2e-16 ***
ORIGIN_GRID_ID2013  1.7759276  0.0232910     76.250  < 2e-16 ***
ORIGIN_GRID_ID2014  2.1802172  0.0232755     93.670  < 2e-16 ***
ORIGIN_GRID_ID2015  2.2734113  0.0233613     97.315  < 2e-16 ***
ORIGIN_GRID_ID2016  2.1805003  0.0232802     93.663  < 2e-16 ***
ORIGIN_GRID_ID2017  2.1440099  0.0232835     92.083  < 2e-16 ***
ORIGIN_GRID_ID2021  2.4326598  0.0234564    103.710  < 2e-16 ***
ORIGIN_GRID_ID2038  1.8217558  0.0232679     78.295  < 2e-16 ***
ORIGIN_GRID_ID2039  2.4903814  0.0233053    106.859  < 2e-16 ***
ORIGIN_GRID_ID2040  2.8076810  0.0232533    120.743  < 2e-16 ***
ORIGIN_GRID_ID2041  3.7191905  0.0232455    159.996  < 2e-16 ***
ORIGIN_GRID_ID2042  2.4717801  0.0233290    105.953  < 2e-16 ***
ORIGIN_GRID_ID2043  0.8257158  0.0237177     34.814  < 2e-16 ***
ORIGIN_GRID_ID2044  3.0865601  0.0232472    132.771  < 2e-16 ***
ORIGIN_GRID_ID2064 -0.6076118  0.0248453    -24.456  < 2e-16 ***
ORIGIN_GRID_ID2065  1.4575392  0.0233208     62.499  < 2e-16 ***
ORIGIN_GRID_ID2066  1.5399619  0.0233208     66.034  < 2e-16 ***
ORIGIN_GRID_ID2067  2.6217684  0.0232863    112.589  < 2e-16 ***
ORIGIN_GRID_ID2068  2.6893447  0.0232858    115.493  < 2e-16 ***
ORIGIN_GRID_ID2070  2.6701795  0.0233049    114.576  < 2e-16 ***
ORIGIN_GRID_ID2071  2.1686798  0.0233792     92.761  < 2e-16 ***
ORIGIN_GRID_ID2093  1.7939407  0.0232767     77.070  < 2e-16 ***
ORIGIN_GRID_ID2094  2.3709801  0.0233016    101.752  < 2e-16 ***
ORIGIN_GRID_ID2095  2.9202998  0.0233560    125.034  < 2e-16 ***
ORIGIN_GRID_ID2098  1.2577465  0.0235536     53.399  < 2e-16 ***
ORIGIN_GRID_ID2119  1.9271380  0.0233095     82.676  < 2e-16 ***
ORIGIN_GRID_ID2120  1.5808176  0.0233457     67.713  < 2e-16 ***
ORIGIN_GRID_ID2123  1.7550442  0.0232997     75.325  < 2e-16 ***
ORIGIN_GRID_ID2147  2.0417336  0.0232766     87.716  < 2e-16 ***
ORIGIN_GRID_ID2148  2.9081233  0.0232482    125.091  < 2e-16 ***
ORIGIN_GRID_ID2149  2.0006244  0.0233505     85.678  < 2e-16 ***
ORIGIN_GRID_ID2150  0.4024657  0.0235638     17.080  < 2e-16 ***
ORIGIN_GRID_ID2151  1.3688738  0.0233464     58.633  < 2e-16 ***
ORIGIN_GRID_ID2152  2.5728769  0.0233114    110.370  < 2e-16 ***
ORIGIN_GRID_ID2154  2.8478940  0.0233896    121.759  < 2e-16 ***
ORIGIN_GRID_ID2174  1.0862259  0.0234948     46.233  < 2e-16 ***
ORIGIN_GRID_ID2177  3.5300153  0.0232446    151.864  < 2e-16 ***
ORIGIN_GRID_ID2178  2.2812986  0.0232641     98.061  < 2e-16 ***
ORIGIN_GRID_ID2179  2.6418718  0.0232826    113.470  < 2e-16 ***
ORIGIN_GRID_ID2180  3.2308412  0.0233287    138.492  < 2e-16 ***
ORIGIN_GRID_ID2201  2.6028609  0.0232635    111.886  < 2e-16 ***
ORIGIN_GRID_ID2203  2.3498674  0.0234111    100.374  < 2e-16 ***
ORIGIN_GRID_ID2204  0.9878465  0.0234251     42.170  < 2e-16 ***
ORIGIN_GRID_ID2205  1.4454435  0.0232853     62.075  < 2e-16 ***
ORIGIN_GRID_ID2206  3.5972496  0.0232404    154.784  < 2e-16 ***
ORIGIN_GRID_ID2208  3.7563312  0.0232807    161.349  < 2e-16 ***
ORIGIN_GRID_ID2228  1.9948438  0.0232998     85.616  < 2e-16 ***
ORIGIN_GRID_ID2231  1.8946941  0.0232810     81.384  < 2e-16 ***
ORIGIN_GRID_ID2233  3.6903846  0.0232411    158.787  < 2e-16 ***
ORIGIN_GRID_ID2234 -0.2195736  0.0340534     -6.448 1.13e-10 ***
ORIGIN_GRID_ID2235  0.8407031  0.0309856     27.132  < 2e-16 ***
ORIGIN_GRID_ID2254  1.2588093  0.0245617     51.251  < 2e-16 ***
ORIGIN_GRID_ID2255  2.4663953  0.0232970    105.867  < 2e-16 ***
ORIGIN_GRID_ID2256  1.9988611  0.0233090     85.755  < 2e-16 ***
ORIGIN_GRID_ID2257  0.6925462  0.0262417     26.391  < 2e-16 ***
ORIGIN_GRID_ID2259  0.8846585  0.0238598     37.077  < 2e-16 ***
ORIGIN_GRID_ID2260  2.9270535  0.0232539    125.874  < 2e-16 ***
ORIGIN_GRID_ID2261  3.2519805  0.0232498    139.871  < 2e-16 ***
ORIGIN_GRID_ID2262  3.1064292  0.0233620    132.969  < 2e-16 ***
ORIGIN_GRID_ID2281  2.2739217  0.0233886     97.224  < 2e-16 ***
ORIGIN_GRID_ID2282  1.9342778  0.0233454     82.855  < 2e-16 ***
ORIGIN_GRID_ID2283  2.5059306  0.0232688    107.695  < 2e-16 ***
ORIGIN_GRID_ID2285  2.9291685  0.0232593    125.935  < 2e-16 ***
ORIGIN_GRID_ID2286  1.6445416  0.0233589     70.403  < 2e-16 ***
ORIGIN_GRID_ID2287  3.5523317  0.0232402    152.853  < 2e-16 ***
ORIGIN_GRID_ID2288  2.1111806  0.0236431     89.294  < 2e-16 ***
ORIGIN_GRID_ID2310  1.9271760  0.0232966     82.723  < 2e-16 ***
ORIGIN_GRID_ID2312 -0.0403056  0.0255070     -1.580 0.114066    
ORIGIN_GRID_ID2313  2.4057955  0.0232749    103.365  < 2e-16 ***
ORIGIN_GRID_ID2314  3.1201920  0.0232426    134.244  < 2e-16 ***
ORIGIN_GRID_ID2315  2.3361408  0.0232872    100.319  < 2e-16 ***
ORIGIN_GRID_ID2316  3.9878868  0.0232457    171.554  < 2e-16 ***
ORIGIN_GRID_ID2335  0.1157332  0.0255764      4.525 6.04e-06 ***
ORIGIN_GRID_ID2339  2.1126956  0.0233347     90.539  < 2e-16 ***
ORIGIN_GRID_ID2340  2.9749198  0.0232500    127.954  < 2e-16 ***
ORIGIN_GRID_ID2341  2.6055142  0.0232532    112.050  < 2e-16 ***
ORIGIN_GRID_ID2342  2.5709569  0.0232691    110.488  < 2e-16 ***
ORIGIN_GRID_ID2343  2.6914050  0.0233179    115.422  < 2e-16 ***
ORIGIN_GRID_ID2363  1.6104112  0.0234350     68.718  < 2e-16 ***
ORIGIN_GRID_ID2367  2.0907099  0.0233558     89.515  < 2e-16 ***
ORIGIN_GRID_ID2368  2.7631341  0.0232633    118.777  < 2e-16 ***
ORIGIN_GRID_ID2369  2.8522180  0.0232838    122.498  < 2e-16 ***
ORIGIN_GRID_ID2370  3.4745889  0.0232501    149.444  < 2e-16 ***
ORIGIN_GRID_ID2371  3.3153433  0.0232706    142.469  < 2e-16 ***
ORIGIN_GRID_ID2390  2.0633731  0.0233460     88.382  < 2e-16 ***
ORIGIN_GRID_ID2391  1.7004009  0.0233293     72.887  < 2e-16 ***
ORIGIN_GRID_ID2394  1.4355376  0.0236181     60.781  < 2e-16 ***
ORIGIN_GRID_ID2395  3.6743915  0.0232505    158.035  < 2e-16 ***
ORIGIN_GRID_ID2396  3.3955575  0.0232468    146.066  < 2e-16 ***
ORIGIN_GRID_ID2397  2.4973603  0.0233255    107.066  < 2e-16 ***
ORIGIN_GRID_ID2398  2.7269746  0.0233402    116.836  < 2e-16 ***
ORIGIN_GRID_ID2418  1.6936045  0.0233971     72.385  < 2e-16 ***
ORIGIN_GRID_ID2419  1.1835543  0.0235458     50.266  < 2e-16 ***
ORIGIN_GRID_ID2422  2.1729657  0.0240314     90.422  < 2e-16 ***
ORIGIN_GRID_ID2423  2.6575683  0.0233285    113.919  < 2e-16 ***
ORIGIN_GRID_ID2424  3.6975389  0.0232436    159.078  < 2e-16 ***
ORIGIN_GRID_ID2425  3.3851155  0.0232645    145.505  < 2e-16 ***
ORIGIN_GRID_ID2426  3.0239152  0.0235147    128.597  < 2e-16 ***
ORIGIN_GRID_ID2443  2.5736808  0.0233005    110.456  < 2e-16 ***
ORIGIN_GRID_ID2445  2.6862397  0.0232632    115.472  < 2e-16 ***
ORIGIN_GRID_ID2449  3.2883070  0.0233916    140.576  < 2e-16 ***
ORIGIN_GRID_ID2450  3.3400851  0.0232745    143.508  < 2e-16 ***
ORIGIN_GRID_ID2451  3.6968596  0.0232513    158.996  < 2e-16 ***
ORIGIN_GRID_ID2472  0.3381564  0.0293676     11.515  < 2e-16 ***
ORIGIN_GRID_ID2473  2.2184164  0.0233161     95.145  < 2e-16 ***
ORIGIN_GRID_ID2478  2.8215266  0.0232967    121.113  < 2e-16 ***
ORIGIN_GRID_ID2479  1.5599097  0.0239456     65.144  < 2e-16 ***
ORIGIN_GRID_ID2497  2.3894861  0.0232907    102.594  < 2e-16 ***
ORIGIN_GRID_ID2499  2.7408235  0.0233106    117.578  < 2e-16 ***
ORIGIN_GRID_ID2505  3.0517456  0.0233153    130.890  < 2e-16 ***
ORIGIN_GRID_ID2527  2.7742369  0.0232773    119.182  < 2e-16 ***
ORIGIN_GRID_ID2532  3.0490587  0.0233324    130.679  < 2e-16 ***
ORIGIN_GRID_ID2533  3.7769217  0.0234254    161.232  < 2e-16 ***
ORIGIN_GRID_ID2551  2.0857450  0.0233839     89.196  < 2e-16 ***
ORIGIN_GRID_ID2553  2.0628444  0.0235595     87.559  < 2e-16 ***
ORIGIN_GRID_ID2554  0.9198946  0.0240390     38.267  < 2e-16 ***
ORIGIN_GRID_ID2559  3.2254040  0.0233841    137.932  < 2e-16 ***
ORIGIN_GRID_ID2580  2.5391635  0.0232835    109.054  < 2e-16 ***
ORIGIN_GRID_ID2581  2.0111190  0.0234849     85.635  < 2e-16 ***
ORIGIN_GRID_ID2607  3.1327175  0.0232565    134.703  < 2e-16 ***
ORIGIN_GRID_ID2608  1.7233622  0.0235207     73.270  < 2e-16 ***
ORIGIN_GRID_ID2634  3.3187970  0.0232617    142.672  < 2e-16 ***
ORIGIN_GRID_ID2635  3.1622744  0.0232838    135.814  < 2e-16 ***
ORIGIN_GRID_ID2636  2.7602345  0.0233038    118.446  < 2e-16 ***
ORIGIN_GRID_ID2661  2.5132075  0.0232696    108.004  < 2e-16 ***
ORIGIN_GRID_ID2663  3.4264993  0.0232522    147.362  < 2e-16 ***
ORIGIN_GRID_ID2665  2.4356819  0.0233489    104.317  < 2e-16 ***
ORIGIN_GRID_ID2688  2.5130447  0.0232781    107.957  < 2e-16 ***
ORIGIN_GRID_ID2689  2.7228214  0.0232847    116.936  < 2e-16 ***
ORIGIN_GRID_ID2690  1.6727826  0.0233364     71.681  < 2e-16 ***
ORIGIN_GRID_ID2691  3.4156101  0.0232527    146.891  < 2e-16 ***
ORIGIN_GRID_ID2693  3.0207454  0.0232759    129.780  < 2e-16 ***
ORIGIN_GRID_ID2715  3.1755003  0.0232786    136.413  < 2e-16 ***
ORIGIN_GRID_ID2717  1.9316855  0.0232759     82.991  < 2e-16 ***
ORIGIN_GRID_ID2718  2.4032790  0.0233335    102.997  < 2e-16 ***
ORIGIN_GRID_ID2719  3.1573835  0.0232551    135.772  < 2e-16 ***
ORIGIN_GRID_ID2742  2.4016446  0.0233176    102.997  < 2e-16 ***
ORIGIN_GRID_ID2743  1.5168040  0.0237497     63.866  < 2e-16 ***
ORIGIN_GRID_ID2744  2.3028678  0.0232786     98.926  < 2e-16 ***
ORIGIN_GRID_ID2745  2.1870966  0.0232718     93.980  < 2e-16 ***
ORIGIN_GRID_ID2747  2.0901951  0.0233236     89.617  < 2e-16 ***
ORIGIN_GRID_ID2768  2.7779343  0.0232985    119.233  < 2e-16 ***
ORIGIN_GRID_ID2771  3.0506147  0.0232564    131.173  < 2e-16 ***
ORIGIN_GRID_ID2773  2.2185095  0.0232828     95.285  < 2e-16 ***
ORIGIN_GRID_ID2798  1.6113467  0.0233794     68.922  < 2e-16 ***
ORIGIN_GRID_ID2799  2.3671349  0.0232650    101.747  < 2e-16 ***
ORIGIN_GRID_ID2800  2.1859692  0.0232872     93.870  < 2e-16 ***
ORIGIN_GRID_ID2824  1.9114884  0.0233830     81.747  < 2e-16 ***
ORIGIN_GRID_ID2825  2.4680253  0.0232596    106.108  < 2e-16 ***
ORIGIN_GRID_ID2826  2.6448252  0.0233075    113.475  < 2e-16 ***
ORIGIN_GRID_ID2827  2.8388307  0.0232762    121.963  < 2e-16 ***
ORIGIN_GRID_ID2852  2.6916579  0.0232897    115.573  < 2e-16 ***
ORIGIN_GRID_ID2853  2.7391416  0.0232544    117.790  < 2e-16 ***
ORIGIN_GRID_ID2854  2.7550418  0.0232617    118.437  < 2e-16 ***
ORIGIN_GRID_ID2878  1.7776630  0.0233728     76.057  < 2e-16 ***
ORIGIN_GRID_ID2879  2.4971335  0.0232854    107.240  < 2e-16 ***
ORIGIN_GRID_ID2880  2.3470540  0.0232863    100.791  < 2e-16 ***
ORIGIN_GRID_ID2881  2.7995523  0.0232697    120.309  < 2e-16 ***
ORIGIN_GRID_ID2907  2.4026869  0.0233183    103.038  < 2e-16 ***
ORIGIN_GRID_ID2908  2.7636259  0.0232838    118.693  < 2e-16 ***
ORIGIN_GRID_ID2933  0.5876302  0.0245071     23.978  < 2e-16 ***
ORIGIN_GRID_ID2934  2.0339225  0.0233346     87.163  < 2e-16 ***
ORIGIN_GRID_ID3098  1.9925089  0.0238063     83.697  < 2e-16 ***
DESTIN_GRID_ID718   0.1939630  0.0045000     43.102  < 2e-16 ***
DESTIN_GRID_ID745  -1.9559822  0.0051019   -383.386  < 2e-16 ***
DESTIN_GRID_ID746  -0.8431058  0.0047009   -179.350  < 2e-16 ***
DESTIN_GRID_ID772  -0.0103535  0.0043724     -2.368 0.017888 *  
DESTIN_GRID_ID799   0.2714899  0.0044436     61.097  < 2e-16 ***
DESTIN_GRID_ID800  -1.0157489  0.0044937   -226.036  < 2e-16 ***
DESTIN_GRID_ID826   1.2462457  0.0043601    285.832  < 2e-16 ***
DESTIN_GRID_ID827   0.1439701  0.0045860     31.393  < 2e-16 ***
DESTIN_GRID_ID854  -1.1585449  0.0048254   -240.094  < 2e-16 ***
DESTIN_GRID_ID880  -1.7818409  0.0054383   -327.649  < 2e-16 ***
DESTIN_GRID_ID881  -1.1492649  0.0054507   -210.846  < 2e-16 ***
DESTIN_GRID_ID908  -0.6705867  0.0046061   -145.586  < 2e-16 ***
DESTIN_GRID_ID934  -0.5466286  0.0046180   -118.369  < 2e-16 ***
DESTIN_GRID_ID935  -0.7843636  0.0047031   -166.777  < 2e-16 ***
DESTIN_GRID_ID961  -0.9643370  0.0048347   -199.463  < 2e-16 ***
DESTIN_GRID_ID962   1.3762836  0.0044246    311.054  < 2e-16 ***
DESTIN_GRID_ID987   0.3442136  0.0045181     76.186  < 2e-16 ***
DESTIN_GRID_ID988  -1.9248493  0.0053686   -358.537  < 2e-16 ***
DESTIN_GRID_ID989  -0.5694922  0.0046410   -122.709  < 2e-16 ***
DESTIN_GRID_ID1015 -3.3700135  0.0094631   -356.121  < 2e-16 ***
DESTIN_GRID_ID1016 -1.5518970  0.0049230   -315.232  < 2e-16 ***
DESTIN_GRID_ID1043 -0.6831876  0.0051383   -132.959  < 2e-16 ***
DESTIN_GRID_ID1068 -2.9583412  0.0210832   -140.318  < 2e-16 ***
DESTIN_GRID_ID1070 -0.3033850  0.0045799    -66.243  < 2e-16 ***
DESTIN_GRID_ID1096 -0.8085900  0.0046659   -173.297  < 2e-16 ***
DESTIN_GRID_ID1097 -1.2604768  0.0051480   -244.849  < 2e-16 ***
DESTIN_GRID_ID1099 -1.0631553  0.0047785   -222.488  < 2e-16 ***
DESTIN_GRID_ID1122 -0.0580064  0.0048865    -11.871  < 2e-16 ***
DESTIN_GRID_ID1123  0.9077222  0.0044398    204.450  < 2e-16 ***
DESTIN_GRID_ID1124 -0.4316917  0.0046813    -92.217  < 2e-16 ***
DESTIN_GRID_ID1125 -1.2802741  0.0051377   -249.191  < 2e-16 ***
DESTIN_GRID_ID1127 -1.8913024  0.0048658   -388.692  < 2e-16 ***
DESTIN_GRID_ID1128 -0.7626245  0.0050973   -149.614  < 2e-16 ***
DESTIN_GRID_ID1148 -1.1056233  0.0052638   -210.043  < 2e-16 ***
DESTIN_GRID_ID1150 -0.3502590  0.0046272    -75.696  < 2e-16 ***
DESTIN_GRID_ID1151 -1.1369884  0.0048006   -236.843  < 2e-16 ***
DESTIN_GRID_ID1152 -1.2269287  0.0054611   -224.665  < 2e-16 ***
DESTIN_GRID_ID1153 -1.5847812  0.0048145   -329.168  < 2e-16 ***
DESTIN_GRID_ID1154  0.6882385  0.0045528    151.169  < 2e-16 ***
DESTIN_GRID_ID1155 -4.0233552  0.0177963   -226.079  < 2e-16 ***
DESTIN_GRID_ID1176 -0.1203867  0.0046446    -25.920  < 2e-16 ***
DESTIN_GRID_ID1178 -1.1483846  0.0047482   -241.855  < 2e-16 ***
DESTIN_GRID_ID1179 -2.0741748  0.0053499   -387.704  < 2e-16 ***
DESTIN_GRID_ID1180 -3.5638436  0.0110307   -323.084  < 2e-16 ***
DESTIN_GRID_ID1181 -0.8496531  0.0046321   -183.425  < 2e-16 ***
DESTIN_GRID_ID1182 -1.2994849  0.0049043   -264.971  < 2e-16 ***
DESTIN_GRID_ID1183 -1.1826692  0.0066387   -178.147  < 2e-16 ***
DESTIN_GRID_ID1205  0.7349495  0.0044885    163.740  < 2e-16 ***
DESTIN_GRID_ID1206 -0.7932483  0.0047973   -165.352  < 2e-16 ***
DESTIN_GRID_ID1207 -1.2141305  0.0049219   -246.680  < 2e-16 ***
DESTIN_GRID_ID1209  0.4186346  0.0046561     89.912  < 2e-16 ***
DESTIN_GRID_ID1232 -0.2341347  0.0045934    -50.972  < 2e-16 ***
DESTIN_GRID_ID1233  0.1571026  0.0047741     32.907  < 2e-16 ***
DESTIN_GRID_ID1235 -0.0768089  0.0046873    -16.387  < 2e-16 ***
DESTIN_GRID_ID1255  0.3490401  0.0070283     49.662  < 2e-16 ***
DESTIN_GRID_ID1258  0.6847276  0.0046384    147.620  < 2e-16 ***
DESTIN_GRID_ID1259 -1.0628248  0.0050139   -211.977  < 2e-16 ***
DESTIN_GRID_ID1261 -1.2643990  0.0049121   -257.405  < 2e-16 ***
DESTIN_GRID_ID1262 -0.5318336  0.0047573   -111.794  < 2e-16 ***
DESTIN_GRID_ID1283 -0.8941125  0.0050343   -177.604  < 2e-16 ***
DESTIN_GRID_ID1284 -1.2168191  0.0062607   -194.357  < 2e-16 ***
DESTIN_GRID_ID1286 -1.7700533  0.0061850   -286.183  < 2e-16 ***
DESTIN_GRID_ID1289 -0.1648277  0.0045940    -35.879  < 2e-16 ***
DESTIN_GRID_ID1309  0.7247845  0.0047206    153.536  < 2e-16 ***
DESTIN_GRID_ID1310  1.4309340  0.0044877    318.854  < 2e-16 ***
DESTIN_GRID_ID1315  0.6606408  0.0045399    145.519  < 2e-16 ***
DESTIN_GRID_ID1316 -1.7778576  0.0056738   -313.344  < 2e-16 ***
DESTIN_GRID_ID1337 -0.6827407  0.0047493   -143.755  < 2e-16 ***
DESTIN_GRID_ID1338 -1.2825409  0.0072070   -177.957  < 2e-16 ***
DESTIN_GRID_ID1343 -1.6173423  0.0051786   -312.311  < 2e-16 ***
DESTIN_GRID_ID1363  0.4692502  0.0048703     96.350  < 2e-16 ***
DESTIN_GRID_ID1364 -1.0216080  0.0051857   -197.006  < 2e-16 ***
DESTIN_GRID_ID1366 -0.4349455  0.0050467    -86.184  < 2e-16 ***
DESTIN_GRID_ID1369 -0.4421142  0.0048059    -91.995  < 2e-16 ***
DESTIN_GRID_ID1370 -0.4061041  0.0049309    -82.359  < 2e-16 ***
DESTIN_GRID_ID1374 -1.3241338  0.0054694   -242.098  < 2e-16 ***
DESTIN_GRID_ID1375 -1.2446840  0.0071582   -173.882  < 2e-16 ***
DESTIN_GRID_ID1391 -0.6577526  0.0058005   -113.395  < 2e-16 ***
DESTIN_GRID_ID1392 -1.6111845  0.0077747   -207.234  < 2e-16 ***
DESTIN_GRID_ID1396 -2.2051999  0.0093305   -236.342  < 2e-16 ***
DESTIN_GRID_ID1397 -1.1968352  0.0050624   -236.419  < 2e-16 ***
DESTIN_GRID_ID1401  0.9141963  0.0047731    191.531  < 2e-16 ***
DESTIN_GRID_ID1402 -0.3552250  0.0049062    -72.403  < 2e-16 ***
DESTIN_GRID_ID1423 -0.9226478  0.0060270   -153.086  < 2e-16 ***
DESTIN_GRID_ID1428 -1.0110822  0.0051686   -195.619  < 2e-16 ***
DESTIN_GRID_ID1429 -0.6547075  0.0052883   -123.803  < 2e-16 ***
DESTIN_GRID_ID1455 -0.9343156  0.0052218   -178.927  < 2e-16 ***
DESTIN_GRID_ID1456 -1.2035246  0.0051065   -235.683  < 2e-16 ***
DESTIN_GRID_ID1471  0.0595355  0.0051619     11.534  < 2e-16 ***
DESTIN_GRID_ID1482  0.4403117  0.0047434     92.827  < 2e-16 ***
DESTIN_GRID_ID1499 -0.9651980  0.0063616   -151.722  < 2e-16 ***
DESTIN_GRID_ID1509 -1.4048423  0.0064665   -217.251  < 2e-16 ***
DESTIN_GRID_ID1510  1.5382317  0.0046590    330.164  < 2e-16 ***
DESTIN_GRID_ID1525  0.6700570  0.0046866    142.974  < 2e-16 ***
DESTIN_GRID_ID1536 -0.0849082  0.0047742    -17.785  < 2e-16 ***
DESTIN_GRID_ID1537 -0.5354499  0.0052001   -102.970  < 2e-16 ***
DESTIN_GRID_ID1552 -2.0647812  0.0103735   -199.043  < 2e-16 ***
DESTIN_GRID_ID1553 -0.7673655  0.0053461   -143.538  < 2e-16 ***
DESTIN_GRID_ID1563 -0.0399330  0.0050428     -7.919 2.40e-15 ***
DESTIN_GRID_ID1564 -0.5183884  0.0047737   -108.593  < 2e-16 ***
DESTIN_GRID_ID1578 -1.5416102  0.0076259   -202.156  < 2e-16 ***
DESTIN_GRID_ID1579  0.8199463  0.0047729    171.791  < 2e-16 ***
DESTIN_GRID_ID1590 -0.3798816  0.0048871    -77.731  < 2e-16 ***
DESTIN_GRID_ID1591 -0.2205259  0.0048746    -45.240  < 2e-16 ***
DESTIN_GRID_ID1605  0.1684055  0.0049260     34.187  < 2e-16 ***
DESTIN_GRID_ID1606 -0.1242133  0.0049663    -25.011  < 2e-16 ***
DESTIN_GRID_ID1617 -1.3957954  0.0078941   -176.815  < 2e-16 ***
DESTIN_GRID_ID1618  1.2365958  0.0046719    264.689  < 2e-16 ***
DESTIN_GRID_ID1631 -0.2589126  0.0053224    -48.646  < 2e-16 ***
DESTIN_GRID_ID1632 -0.1208270  0.0050282    -24.030  < 2e-16 ***
DESTIN_GRID_ID1634 -0.0584135  0.0060981     -9.579  < 2e-16 ***
DESTIN_GRID_ID1644 -0.3328473  0.0050330    -66.133  < 2e-16 ***
DESTIN_GRID_ID1645  0.0180575  0.0048378      3.733 0.000190 ***
DESTIN_GRID_ID1658 -0.4682274  0.0054852    -85.361  < 2e-16 ***
DESTIN_GRID_ID1659  0.4154073  0.0047176     88.055  < 2e-16 ***
DESTIN_GRID_ID1672 -0.6442192  0.0056607   -113.805  < 2e-16 ***
DESTIN_GRID_ID1684  0.3105462  0.0049439     62.814  < 2e-16 ***
DESTIN_GRID_ID1685 -0.0014060  0.0054850     -0.256 0.797690    
DESTIN_GRID_ID1686  0.0445936  0.0049399      9.027  < 2e-16 ***
DESTIN_GRID_ID1688 -0.6327589  0.0073481    -86.112  < 2e-16 ***
DESTIN_GRID_ID1699 -0.4353885  0.0049091    -88.690  < 2e-16 ***
DESTIN_GRID_ID1700 -0.9073130  0.0074334   -122.059  < 2e-16 ***
DESTIN_GRID_ID1712 -1.1478478  0.0058805   -195.195  < 2e-16 ***
DESTIN_GRID_ID1713  0.7988942  0.0046445    172.007  < 2e-16 ***
DESTIN_GRID_ID1727  0.0328131  0.0048716      6.736 1.63e-11 ***
DESTIN_GRID_ID1739  0.8438095  0.0046105    183.018  < 2e-16 ***
DESTIN_GRID_ID1753  1.0432879  0.0046858    222.648  < 2e-16 ***
DESTIN_GRID_ID1754 -0.6124385  0.0051839   -118.143  < 2e-16 ***
DESTIN_GRID_ID1766  0.3649578  0.0047378     77.031  < 2e-16 ***
DESTIN_GRID_ID1767  0.2335433  0.0046878     49.820  < 2e-16 ***
DESTIN_GRID_ID1780 -0.7583507  0.0109615    -69.183  < 2e-16 ***
DESTIN_GRID_ID1781 -0.6664453  0.0050283   -132.539  < 2e-16 ***
DESTIN_GRID_ID1792 -0.6686807  0.0052744   -126.778  < 2e-16 ***
DESTIN_GRID_ID1793  0.4518009  0.0046641     96.867  < 2e-16 ***
DESTIN_GRID_ID1794 -0.5108334  0.0055470    -92.091  < 2e-16 ***
DESTIN_GRID_ID1807 -1.7750315  0.0055653   -318.943  < 2e-16 ***
DESTIN_GRID_ID1820 -0.2884589  0.0050978    -56.585  < 2e-16 ***
DESTIN_GRID_ID1821  1.4291796  0.0046038    310.435  < 2e-16 ***
DESTIN_GRID_ID1833  0.2248939  0.0047092     47.756  < 2e-16 ***
DESTIN_GRID_ID1835 -1.3808991  0.0057186   -241.477  < 2e-16 ***
DESTIN_GRID_ID1847 -1.7201695  0.0101969   -168.696  < 2e-16 ***
DESTIN_GRID_ID1854 -0.6312645  0.0055800   -113.131  < 2e-16 ***
DESTIN_GRID_ID1859 -1.1490823  0.0049002   -234.497  < 2e-16 ***
DESTIN_GRID_ID1860 -0.9450653  0.0049396   -191.324  < 2e-16 ***
DESTIN_GRID_ID1861 -0.9881242  0.0056202   -175.817  < 2e-16 ***
DESTIN_GRID_ID1874  0.1019648  0.0048983     20.816  < 2e-16 ***
DESTIN_GRID_ID1875  0.3601037  0.0046948     76.703  < 2e-16 ***
DESTIN_GRID_ID1882  0.1511885  0.0047652     31.727  < 2e-16 ***
DESTIN_GRID_ID1883 -1.2206459  0.0057340   -212.878  < 2e-16 ***
DESTIN_GRID_ID1886  1.1076412  0.0046601    237.685  < 2e-16 ***
DESTIN_GRID_ID1887  1.1457362  0.0046469    246.557  < 2e-16 ***
DESTIN_GRID_ID1888 -1.1284323  0.0056013   -201.459  < 2e-16 ***
DESTIN_GRID_ID1905 -0.9750532  0.0058148   -167.686  < 2e-16 ***
DESTIN_GRID_ID1907 -0.0731515  0.0049999    -14.630  < 2e-16 ***
DESTIN_GRID_ID1908 -0.9511307  0.0054011   -176.100  < 2e-16 ***
DESTIN_GRID_ID1909 -0.6378764  0.0049965   -127.664  < 2e-16 ***
DESTIN_GRID_ID1912 -3.9575939  0.0214447   -184.549  < 2e-16 ***
DESTIN_GRID_ID1913 -0.7798404  0.0048808   -159.778  < 2e-16 ***
DESTIN_GRID_ID1914 -0.4005485  0.0047984    -83.475  < 2e-16 ***
DESTIN_GRID_ID1928 -0.0590015  0.0052084    -11.328  < 2e-16 ***
DESTIN_GRID_ID1929  0.0174913  0.0052645      3.323 0.000892 ***
DESTIN_GRID_ID1933  0.3864590  0.0047682     81.049  < 2e-16 ***
DESTIN_GRID_ID1935 -0.2239167  0.0049718    -45.038  < 2e-16 ***
DESTIN_GRID_ID1936 -0.6146990  0.0049502   -124.177  < 2e-16 ***
DESTIN_GRID_ID1937 -0.5040551  0.0049798   -101.221  < 2e-16 ***
DESTIN_GRID_ID1940 -1.0568233  0.0049870   -211.917  < 2e-16 ***
DESTIN_GRID_ID1941 -2.2416149  0.0055077   -406.998  < 2e-16 ***
DESTIN_GRID_ID1942 -1.0735463  0.0063656   -168.647  < 2e-16 ***
DESTIN_GRID_ID1955  1.1229461  0.0047179    238.018  < 2e-16 ***
DESTIN_GRID_ID1959  0.2842657  0.0047588     59.735  < 2e-16 ***
DESTIN_GRID_ID1960  0.4658091  0.0046866     99.392  < 2e-16 ***
DESTIN_GRID_ID1962 -0.8926516  0.0050414   -177.065  < 2e-16 ***
DESTIN_GRID_ID1963 -1.0839692  0.0049669   -218.238  < 2e-16 ***
DESTIN_GRID_ID1967 -0.6886420  0.0048970   -140.626  < 2e-16 ***
DESTIN_GRID_ID1968 -0.8951445  0.0050966   -175.634  < 2e-16 ***
DESTIN_GRID_ID1985  0.2185709  0.0050481     43.297  < 2e-16 ***
DESTIN_GRID_ID1987  1.0136481  0.0045913    220.778  < 2e-16 ***
DESTIN_GRID_ID1988 -0.9201083  0.0051213   -179.662  < 2e-16 ***
DESTIN_GRID_ID1989 -1.1682897  0.0053480   -218.455  < 2e-16 ***
DESTIN_GRID_ID1990  1.4942379  0.0045773    326.446  < 2e-16 ***
DESTIN_GRID_ID1994 -3.2545787  0.0132423   -245.771  < 2e-16 ***
DESTIN_GRID_ID1995 -1.5189196  0.0051641   -294.130  < 2e-16 ***
DESTIN_GRID_ID2010  0.5775777  0.0046546    124.088  < 2e-16 ***
DESTIN_GRID_ID2011  0.5477057  0.0047683    114.863  < 2e-16 ***
DESTIN_GRID_ID2012 -0.7511628  0.0054037   -139.009  < 2e-16 ***
DESTIN_GRID_ID2013 -0.6447981  0.0048043   -134.213  < 2e-16 ***
DESTIN_GRID_ID2014 -0.4773138  0.0047689   -100.089  < 2e-16 ***
DESTIN_GRID_ID2015  0.2116949  0.0050317     42.072  < 2e-16 ***
DESTIN_GRID_ID2016 -0.6643204  0.0048736   -136.309  < 2e-16 ***
DESTIN_GRID_ID2017 -0.7211582  0.0048654   -148.223  < 2e-16 ***
DESTIN_GRID_ID2021 -2.8838388  0.0078376   -367.948  < 2e-16 ***
DESTIN_GRID_ID2038  1.1313977  0.0046014    245.881  < 2e-16 ***
DESTIN_GRID_ID2039 -0.4370019  0.0053553    -81.601  < 2e-16 ***
DESTIN_GRID_ID2040 -0.2542374  0.0049414    -51.451  < 2e-16 ***
DESTIN_GRID_ID2041  0.3243669  0.0047197     68.726  < 2e-16 ***
DESTIN_GRID_ID2042 -0.3113401  0.0053442    -58.258  < 2e-16 ***
DESTIN_GRID_ID2043 -0.1130782  0.0049661    -22.770  < 2e-16 ***
DESTIN_GRID_ID2044 -0.4901194  0.0047618   -102.927  < 2e-16 ***
DESTIN_GRID_ID2064  0.3073836  0.0049824     61.694  < 2e-16 ***
DESTIN_GRID_ID2065 -0.0411775  0.0049786     -8.271  < 2e-16 ***
DESTIN_GRID_ID2066 -0.2404425  0.0047637    -50.474  < 2e-16 ***
DESTIN_GRID_ID2067 -0.9065893  0.0052949   -171.218  < 2e-16 ***
DESTIN_GRID_ID2068 -0.6963177  0.0050601   -137.609  < 2e-16 ***
DESTIN_GRID_ID2070 -0.1997319  0.0050346    -39.672  < 2e-16 ***
DESTIN_GRID_ID2071 -0.1727846  0.0048699    -35.480  < 2e-16 ***
DESTIN_GRID_ID2093  0.3301950  0.0046960     70.315  < 2e-16 ***
DESTIN_GRID_ID2094 -0.0031050  0.0047971     -0.647 0.517460    
DESTIN_GRID_ID2095 -0.4780985  0.0052813    -90.527  < 2e-16 ***
DESTIN_GRID_ID2098 -0.5364615  0.0051393   -104.385  < 2e-16 ***
DESTIN_GRID_ID2119  0.0133360  0.0049685      2.684 0.007272 ** 
DESTIN_GRID_ID2120  0.6005505  0.0047395    126.711  < 2e-16 ***
DESTIN_GRID_ID2123 -1.2610912  0.0054262   -232.408  < 2e-16 ***
DESTIN_GRID_ID2147  0.2408176  0.0047518     50.680  < 2e-16 ***
DESTIN_GRID_ID2148  0.0719282  0.0047881     15.022  < 2e-16 ***
DESTIN_GRID_ID2149  0.2929158  0.0048743     60.094  < 2e-16 ***
DESTIN_GRID_ID2150 -1.8725654  0.0073536   -254.645  < 2e-16 ***
DESTIN_GRID_ID2151 -2.2245516  0.0067431   -329.902  < 2e-16 ***
DESTIN_GRID_ID2152  0.1064571  0.0047331     22.492  < 2e-16 ***
DESTIN_GRID_ID2154 -2.1859002  0.0063673   -343.299  < 2e-16 ***
DESTIN_GRID_ID2174 -1.6131427  0.0064744   -249.157  < 2e-16 ***
DESTIN_GRID_ID2177  1.7197299  0.0045647    376.746  < 2e-16 ***
DESTIN_GRID_ID2178 -1.7089307  0.0051468   -332.035  < 2e-16 ***
DESTIN_GRID_ID2179 -0.5252628  0.0047906   -109.645  < 2e-16 ***
DESTIN_GRID_ID2180 -1.4325533  0.0056594   -253.126  < 2e-16 ***
DESTIN_GRID_ID2201 -0.1043766  0.0049155    -21.234  < 2e-16 ***
DESTIN_GRID_ID2203 -0.1483282  0.0055902    -26.534  < 2e-16 ***
DESTIN_GRID_ID2204 -0.2240379  0.0049431    -45.323  < 2e-16 ***
DESTIN_GRID_ID2205 -1.1781786  0.0049202   -239.455  < 2e-16 ***
DESTIN_GRID_ID2206 -0.2396310  0.0046785    -51.220  < 2e-16 ***
DESTIN_GRID_ID2208 -1.0806975  0.0050722   -213.061  < 2e-16 ***
DESTIN_GRID_ID2228 -0.5081807  0.0050621   -100.389  < 2e-16 ***
DESTIN_GRID_ID2231 -0.7044604  0.0049007   -143.748  < 2e-16 ***
DESTIN_GRID_ID2233 -0.3730052  0.0046647    -79.964  < 2e-16 ***
DESTIN_GRID_ID2234 -6.7752068  0.0914051    -74.123  < 2e-16 ***
DESTIN_GRID_ID2235 -3.6687371  0.0316191   -116.029  < 2e-16 ***
DESTIN_GRID_ID2254 -0.2805670  0.0072543    -38.676  < 2e-16 ***
DESTIN_GRID_ID2255 -0.7283025  0.0059103   -123.226  < 2e-16 ***
DESTIN_GRID_ID2256 -0.3364117  0.0050166    -67.060  < 2e-16 ***
DESTIN_GRID_ID2257 -0.8080581  0.0088426    -91.382  < 2e-16 ***
DESTIN_GRID_ID2259 -1.4789130  0.0061339   -241.105  < 2e-16 ***
DESTIN_GRID_ID2260 -1.3142821  0.0048713   -269.799  < 2e-16 ***
DESTIN_GRID_ID2261 -1.1691197  0.0048719   -239.970  < 2e-16 ***
DESTIN_GRID_ID2262 -2.3369395  0.0065255   -358.122  < 2e-16 ***
DESTIN_GRID_ID2281 -0.5517863  0.0058738    -93.939  < 2e-16 ***
DESTIN_GRID_ID2282  0.7459629  0.0047161    158.173  < 2e-16 ***
DESTIN_GRID_ID2283 -0.4762512  0.0050699    -93.937  < 2e-16 ***
DESTIN_GRID_ID2285 -0.0788541  0.0048478    -16.266  < 2e-16 ***
DESTIN_GRID_ID2286 -1.1084388  0.0051132   -216.781  < 2e-16 ***
DESTIN_GRID_ID2287 -0.3521351  0.0046258    -76.124  < 2e-16 ***
DESTIN_GRID_ID2288 -2.8694610  0.0080836   -354.975  < 2e-16 ***
DESTIN_GRID_ID2310 -0.0390598  0.0048324     -8.083 6.33e-16 ***
DESTIN_GRID_ID2312 -1.4312874  0.0066529   -215.136  < 2e-16 ***
DESTIN_GRID_ID2313  0.5722615  0.0046262    123.699  < 2e-16 ***
DESTIN_GRID_ID2314  0.5842860  0.0045749    127.715  < 2e-16 ***
DESTIN_GRID_ID2315 -1.4158281  0.0050521   -280.246  < 2e-16 ***
DESTIN_GRID_ID2316 -0.7534054  0.0047676   -158.025  < 2e-16 ***
DESTIN_GRID_ID2335 -1.8282822  0.0142391   -128.399  < 2e-16 ***
DESTIN_GRID_ID2339 -0.3617199  0.0050173    -72.094  < 2e-16 ***
DESTIN_GRID_ID2340 -0.6687048  0.0047163   -141.785  < 2e-16 ***
DESTIN_GRID_ID2341 -0.4885255  0.0046448   -105.177  < 2e-16 ***
DESTIN_GRID_ID2342 -1.7767328  0.0049416   -359.549  < 2e-16 ***
DESTIN_GRID_ID2343 -1.9848810  0.0057771   -343.578  < 2e-16 ***
DESTIN_GRID_ID2363 -0.8509199  0.0057823   -147.159  < 2e-16 ***
DESTIN_GRID_ID2367 -0.6922879  0.0053537   -129.311  < 2e-16 ***
DESTIN_GRID_ID2368 -0.9268677  0.0048673   -190.429  < 2e-16 ***
DESTIN_GRID_ID2369 -0.0995070  0.0046764    -21.279  < 2e-16 ***
DESTIN_GRID_ID2370  0.6603867  0.0045910    143.845  < 2e-16 ***
DESTIN_GRID_ID2371 -1.1742254  0.0050853   -230.906  < 2e-16 ***
DESTIN_GRID_ID2390  0.7217918  0.0047081    153.308  < 2e-16 ***
DESTIN_GRID_ID2391  0.3462741  0.0047871     72.335  < 2e-16 ***
DESTIN_GRID_ID2394 -2.2954221  0.0073311   -313.107  < 2e-16 ***
DESTIN_GRID_ID2395 -0.8640968  0.0048139   -179.502  < 2e-16 ***
DESTIN_GRID_ID2396 -0.9592654  0.0047111   -203.619  < 2e-16 ***
DESTIN_GRID_ID2397 -2.5477662  0.0070582   -360.966  < 2e-16 ***
DESTIN_GRID_ID2398 -1.7965174  0.0058252   -308.404  < 2e-16 ***
DESTIN_GRID_ID2418 -0.2451402  0.0051618    -47.491  < 2e-16 ***
DESTIN_GRID_ID2419  0.3712626  0.0049122     75.580  < 2e-16 ***
DESTIN_GRID_ID2422 -1.9709831  0.0100976   -195.193  < 2e-16 ***
DESTIN_GRID_ID2423 -1.9517100  0.0055356   -352.572  < 2e-16 ***
DESTIN_GRID_ID2424 -0.5646134  0.0047048   -120.007  < 2e-16 ***
DESTIN_GRID_ID2425  0.7372145  0.0046393    158.907  < 2e-16 ***
DESTIN_GRID_ID2426 -0.9783510  0.0062876   -155.601  < 2e-16 ***
DESTIN_GRID_ID2443  0.7794982  0.0047647    163.600  < 2e-16 ***
DESTIN_GRID_ID2445  0.1994319  0.0047932     41.607  < 2e-16 ***
DESTIN_GRID_ID2449 -2.0714702  0.0074849   -276.752  < 2e-16 ***
DESTIN_GRID_ID2450 -1.6894065  0.0051015   -331.162  < 2e-16 ***
DESTIN_GRID_ID2451 -0.2678737  0.0046636    -57.439  < 2e-16 ***
DESTIN_GRID_ID2472 -2.3071911  0.0167683   -137.593  < 2e-16 ***
DESTIN_GRID_ID2473  0.2086822  0.0049329     42.305  < 2e-16 ***
DESTIN_GRID_ID2478 -1.5162414  0.0051226   -295.993  < 2e-16 ***
DESTIN_GRID_ID2479 -2.3124779  0.0088916   -260.074  < 2e-16 ***
DESTIN_GRID_ID2497 -0.2848716  0.0050392    -56.531  < 2e-16 ***
DESTIN_GRID_ID2499 -0.9087378  0.0058029   -156.602  < 2e-16 ***
DESTIN_GRID_ID2505 -1.3559996  0.0053161   -255.072  < 2e-16 ***
DESTIN_GRID_ID2527  0.5922697  0.0047202    125.474  < 2e-16 ***
DESTIN_GRID_ID2532 -2.0128350  0.0061219   -328.791  < 2e-16 ***
DESTIN_GRID_ID2533 -1.8035976  0.0078502   -229.753  < 2e-16 ***
DESTIN_GRID_ID2551 -0.2530546  0.0056560    -44.741  < 2e-16 ***
DESTIN_GRID_ID2553 -1.2244979  0.0071391   -171.520  < 2e-16 ***
DESTIN_GRID_ID2554 -1.8271344  0.0083560   -218.661  < 2e-16 ***
DESTIN_GRID_ID2559 -1.9311098  0.0072295   -267.113  < 2e-16 ***
DESTIN_GRID_ID2580 -0.2987122  0.0049364    -60.512  < 2e-16 ***
DESTIN_GRID_ID2581 -1.2020103  0.0066416   -180.983  < 2e-16 ***
DESTIN_GRID_ID2607 -0.7237964  0.0050085   -144.514  < 2e-16 ***
DESTIN_GRID_ID2608 -1.3599631  0.0069627   -195.322  < 2e-16 ***
DESTIN_GRID_ID2634  1.5599522  0.0046153    337.994  < 2e-16 ***
DESTIN_GRID_ID2635 -1.1351974  0.0056533   -200.802  < 2e-16 ***
DESTIN_GRID_ID2636 -0.0692076  0.0049973    -13.849  < 2e-16 ***
DESTIN_GRID_ID2661 -0.8285481  0.0049164   -168.528  < 2e-16 ***
DESTIN_GRID_ID2663  0.1038898  0.0047388     21.923  < 2e-16 ***
DESTIN_GRID_ID2665  0.1104610  0.0048242     22.897  < 2e-16 ***
DESTIN_GRID_ID2688 -0.6207011  0.0050578   -122.721  < 2e-16 ***
DESTIN_GRID_ID2689  0.3201680  0.0047583     67.287  < 2e-16 ***
DESTIN_GRID_ID2690 -0.2145571  0.0048192    -44.521  < 2e-16 ***
DESTIN_GRID_ID2691 -0.4468812  0.0048309    -92.504  < 2e-16 ***
DESTIN_GRID_ID2693 -0.2024323  0.0049391    -40.985  < 2e-16 ***
DESTIN_GRID_ID2715 -0.5661025  0.0052168   -108.514  < 2e-16 ***
DESTIN_GRID_ID2717 -0.4933704  0.0047412   -104.060  < 2e-16 ***
DESTIN_GRID_ID2718 -1.5069439  0.0058608   -257.123  < 2e-16 ***
DESTIN_GRID_ID2719 -0.3936952  0.0048052    -81.931  < 2e-16 ***
DESTIN_GRID_ID2742 -0.3787101  0.0050032    -75.693  < 2e-16 ***
DESTIN_GRID_ID2743 -0.2526386  0.0056970    -44.346  < 2e-16 ***
DESTIN_GRID_ID2744  0.3348967  0.0047285     70.825  < 2e-16 ***
DESTIN_GRID_ID2745 -0.0216497  0.0047435     -4.564 5.02e-06 ***
DESTIN_GRID_ID2747 -1.2068428  0.0053891   -223.943  < 2e-16 ***
DESTIN_GRID_ID2768 -0.2874155  0.0050754    -56.629  < 2e-16 ***
DESTIN_GRID_ID2771  1.7384085  0.0046039    377.598  < 2e-16 ***
DESTIN_GRID_ID2773 -1.2621387  0.0051466   -245.236  < 2e-16 ***
DESTIN_GRID_ID2798 -1.5200881  0.0061954   -245.356  < 2e-16 ***
DESTIN_GRID_ID2799 -0.6770829  0.0049245   -137.491  < 2e-16 ***
DESTIN_GRID_ID2800  0.6831949  0.0046594    146.628  < 2e-16 ***
DESTIN_GRID_ID2824  0.8153328  0.0048106    169.486  < 2e-16 ***
DESTIN_GRID_ID2825 -0.3184101  0.0047711    -66.737  < 2e-16 ***
DESTIN_GRID_ID2826 -0.8280730  0.0054883   -150.881  < 2e-16 ***
DESTIN_GRID_ID2827  1.3804977  0.0046424    297.366  < 2e-16 ***
DESTIN_GRID_ID2852 -0.5717200  0.0054610   -104.691  < 2e-16 ***
DESTIN_GRID_ID2853  0.7391529  0.0046355    159.456  < 2e-16 ***
DESTIN_GRID_ID2854 -0.1054111  0.0048181    -21.878  < 2e-16 ***
DESTIN_GRID_ID2878 -0.5644096  0.0054179   -104.175  < 2e-16 ***
DESTIN_GRID_ID2879 -0.4541410  0.0049990    -90.846  < 2e-16 ***
DESTIN_GRID_ID2880 -1.1765311  0.0053492   -219.946  < 2e-16 ***
DESTIN_GRID_ID2881 -0.6554680  0.0051526   -127.211  < 2e-16 ***
DESTIN_GRID_ID2907 -1.1725359  0.0060105   -195.081  < 2e-16 ***
DESTIN_GRID_ID2908 -0.0956805  0.0048605    -19.685  < 2e-16 ***
DESTIN_GRID_ID2933  0.8832728  0.0051354    171.995  < 2e-16 ***
DESTIN_GRID_ID2934 -0.7921841  0.0052797   -150.043  < 2e-16 ***
DESTIN_GRID_ID3098  0.3770330  0.0054613     69.037  < 2e-16 ***
log(DISTANCE)      -1.5164188  0.0001409 -10764.473  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 514012584  on 101667  degrees of freedom
Residual deviance:  94904454  on 100972  degrees of freedom
AIC: 95663455

Number of Fisher Scoring iterations: 6
CalcRSquared(dbcSIM_Poisson2$data$TRIPS, dbcSIM_Poisson2$fitted.values)
[1] 0.7777153
model_list3 <- list(originConstrained3=orcSIM_Poisson3,
                   destinationConstrained3=decSIM_Poisson3,
                   doublyConstrained2=dbcSIM_Poisson2)
compare_performance(model_list3,
                    metrics = "RMSE")
# Comparison of Model Performance Indices

Name                    | Model |     RMSE
------------------------------------------
originConstrained3      |   glm | 2998.532
destinationConstrained3 |   glm | 3192.761
doublyConstrained2      |   glm | 2302.478

8.1.3 Removing both the variables and outliers

orcSIM_Poisson4 <- glm(formula = TRIPS ~ 
                ORIGIN_GRID_ID +
                log(TDESTIN_BIZ_COUNT) +
                log(TDESTIN_FINSERV_COUNT) +
                  log(TDESTIN_MRTEXIT_COUNT) +
                  log(TDESTIN_BUSSTOP_COUNT) +
                  log(TDESTIN_HDBCOMM_UNITS) +
                  log(TDESTIN_HDBRES_UNITS) + 
                  log(TDESTIN_SCHOOLS_COUNT) + 
                log(DISTANCE) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow1,
              na.action = na.exclude)
summary(orcSIM_Poisson4)

Call:
glm(formula = TRIPS ~ ORIGIN_GRID_ID + log(TDESTIN_BIZ_COUNT) + 
    log(TDESTIN_FINSERV_COUNT) + log(TDESTIN_MRTEXIT_COUNT) + 
    log(TDESTIN_BUSSTOP_COUNT) + log(TDESTIN_HDBCOMM_UNITS) + 
    log(TDESTIN_HDBRES_UNITS) + log(TDESTIN_SCHOOLS_COUNT) + 
    log(DISTANCE) - 1, family = poisson(link = "log"), data = inter_zonal_flow1, 
    na.action = na.exclude)

Coefficients:
                             Estimate Std. Error  z value Pr(>|z|)    
ORIGIN_GRID_ID664           1.466e+01  2.324e-02    630.7   <2e-16 ***
ORIGIN_GRID_ID718           1.863e+01  1.665e-03  11191.7   <2e-16 ***
ORIGIN_GRID_ID745           1.633e+01  2.758e-03   5921.5   <2e-16 ***
ORIGIN_GRID_ID746           1.836e+01  1.722e-03  10666.1   <2e-16 ***
ORIGIN_GRID_ID772           1.805e+01  1.569e-03  11500.5   <2e-16 ***
ORIGIN_GRID_ID799           1.742e+01  2.440e-03   7137.5   <2e-16 ***
ORIGIN_GRID_ID800           1.715e+01  2.109e-03   8132.1   <2e-16 ***
ORIGIN_GRID_ID826           1.829e+01  1.568e-03  11663.2   <2e-16 ***
ORIGIN_GRID_ID827           1.832e+01  1.810e-03  10118.8   <2e-16 ***
ORIGIN_GRID_ID854           1.715e+01  2.258e-03   7596.0   <2e-16 ***
ORIGIN_GRID_ID880           1.656e+01  2.925e-03   5659.1   <2e-16 ***
ORIGIN_GRID_ID881           1.584e+01  6.075e-03   2607.7   <2e-16 ***
ORIGIN_GRID_ID908           1.807e+01  1.637e-03  11036.5   <2e-16 ***
ORIGIN_GRID_ID934           1.675e+01  2.384e-03   7024.3   <2e-16 ***
ORIGIN_GRID_ID935           1.750e+01  1.863e-03   9394.8   <2e-16 ***
ORIGIN_GRID_ID961           1.787e+01  1.849e-03   9660.2   <2e-16 ***
ORIGIN_GRID_ID962           1.809e+01  1.659e-03  10904.3   <2e-16 ***
ORIGIN_GRID_ID987           1.841e+01  1.656e-03  11113.5   <2e-16 ***
ORIGIN_GRID_ID988           1.689e+01  2.428e-03   6956.2   <2e-16 ***
ORIGIN_GRID_ID989           1.803e+01  1.628e-03  11077.7   <2e-16 ***
ORIGIN_GRID_ID1015          1.683e+01  3.045e-03   5527.7   <2e-16 ***
ORIGIN_GRID_ID1016          1.703e+01  2.030e-03   8390.9   <2e-16 ***
ORIGIN_GRID_ID1043          1.725e+01  2.803e-03   6154.6   <2e-16 ***
ORIGIN_GRID_ID1068          1.486e+01  1.914e-02    776.5   <2e-16 ***
ORIGIN_GRID_ID1070          1.749e+01  1.857e-03   9420.1   <2e-16 ***
ORIGIN_GRID_ID1096          1.702e+01  1.909e-03   8916.1   <2e-16 ***
ORIGIN_GRID_ID1097          1.685e+01  2.627e-03   6413.5   <2e-16 ***
ORIGIN_GRID_ID1099          1.834e+01  1.656e-03  11077.1   <2e-16 ***
ORIGIN_GRID_ID1122          1.797e+01  1.719e-03  10450.6   <2e-16 ***
ORIGIN_GRID_ID1123          1.768e+01  1.740e-03  10157.8   <2e-16 ***
ORIGIN_GRID_ID1124          1.704e+01  2.188e-03   7787.5   <2e-16 ***
ORIGIN_GRID_ID1125          1.764e+01  2.044e-03   8627.3   <2e-16 ***
ORIGIN_GRID_ID1127          1.761e+01  1.699e-03  10367.9   <2e-16 ***
ORIGIN_GRID_ID1128          1.751e+01  2.066e-03   8477.9   <2e-16 ***
ORIGIN_GRID_ID1148          1.654e+01  2.881e-03   5741.0   <2e-16 ***
ORIGIN_GRID_ID1150          1.793e+01  1.568e-03  11430.7   <2e-16 ***
ORIGIN_GRID_ID1151          1.737e+01  1.899e-03   9148.8   <2e-16 ***
ORIGIN_GRID_ID1152          1.756e+01  2.263e-03   7762.0   <2e-16 ***
ORIGIN_GRID_ID1153          1.807e+01  1.775e-03  10179.1   <2e-16 ***
ORIGIN_GRID_ID1154          1.813e+01  1.739e-03  10424.7   <2e-16 ***
ORIGIN_GRID_ID1155          1.488e+01  1.039e-02   1431.7   <2e-16 ***
ORIGIN_GRID_ID1176          1.679e+01  2.454e-03   6842.4   <2e-16 ***
ORIGIN_GRID_ID1178          1.696e+01  1.987e-03   8533.9   <2e-16 ***
ORIGIN_GRID_ID1179          1.668e+01  2.358e-03   7075.9   <2e-16 ***
ORIGIN_GRID_ID1180          1.570e+01  5.508e-03   2850.0   <2e-16 ***
ORIGIN_GRID_ID1181          1.683e+01  1.881e-03   8947.9   <2e-16 ***
ORIGIN_GRID_ID1182          1.771e+01  1.697e-03  10432.2   <2e-16 ***
ORIGIN_GRID_ID1183          1.833e+01  2.360e-03   7765.4   <2e-16 ***
ORIGIN_GRID_ID1205          1.789e+01  1.640e-03  10910.8   <2e-16 ***
ORIGIN_GRID_ID1206          1.704e+01  2.164e-03   7873.1   <2e-16 ***
ORIGIN_GRID_ID1207          1.681e+01  2.734e-03   6150.0   <2e-16 ***
ORIGIN_GRID_ID1209          1.727e+01  2.089e-03   8266.0   <2e-16 ***
ORIGIN_GRID_ID1232          1.765e+01  1.732e-03  10187.9   <2e-16 ***
ORIGIN_GRID_ID1233          1.709e+01  2.833e-03   6032.5   <2e-16 ***
ORIGIN_GRID_ID1235          1.759e+01  2.055e-03   8562.1   <2e-16 ***
ORIGIN_GRID_ID1255          1.614e+01  1.065e-02   1515.8   <2e-16 ***
ORIGIN_GRID_ID1258          1.692e+01  2.986e-03   5666.4   <2e-16 ***
ORIGIN_GRID_ID1259          1.718e+01  2.047e-03   8392.2   <2e-16 ***
ORIGIN_GRID_ID1261          1.679e+01  2.157e-03   7784.9   <2e-16 ***
ORIGIN_GRID_ID1262          1.771e+01  1.796e-03   9859.8   <2e-16 ***
ORIGIN_GRID_ID1283          1.660e+01  2.685e-03   6183.2   <2e-16 ***
ORIGIN_GRID_ID1284          1.716e+01  2.808e-03   6113.7   <2e-16 ***
ORIGIN_GRID_ID1286          1.656e+01  3.776e-03   4385.1   <2e-16 ***
ORIGIN_GRID_ID1289          1.697e+01  1.958e-03   8664.2   <2e-16 ***
ORIGIN_GRID_ID1309          1.817e+01  1.862e-03   9761.0   <2e-16 ***
ORIGIN_GRID_ID1310          1.790e+01  1.680e-03  10654.0   <2e-16 ***
ORIGIN_GRID_ID1315          1.727e+01  1.843e-03   9374.9   <2e-16 ***
ORIGIN_GRID_ID1316          1.615e+01  3.241e-03   4983.1   <2e-16 ***
ORIGIN_GRID_ID1337          1.748e+01  1.777e-03   9834.7   <2e-16 ***
ORIGIN_GRID_ID1338          1.705e+01  5.235e-03   3257.5   <2e-16 ***
ORIGIN_GRID_ID1343          1.668e+01  2.212e-03   7542.5   <2e-16 ***
ORIGIN_GRID_ID1363          1.676e+01  3.258e-03   5143.5   <2e-16 ***
ORIGIN_GRID_ID1364          1.670e+01  2.389e-03   6989.5   <2e-16 ***
ORIGIN_GRID_ID1366          1.694e+01  2.841e-03   5961.2   <2e-16 ***
ORIGIN_GRID_ID1369          1.744e+01  1.744e-03   9999.3   <2e-16 ***
ORIGIN_GRID_ID1370          1.771e+01  1.917e-03   9239.2   <2e-16 ***
ORIGIN_GRID_ID1374          1.650e+01  2.925e-03   5641.1   <2e-16 ***
ORIGIN_GRID_ID1375          1.776e+01  3.309e-03   5365.7   <2e-16 ***
ORIGIN_GRID_ID1391          1.576e+01  4.835e-03   3260.1   <2e-16 ***
ORIGIN_GRID_ID1392          1.606e+01  3.917e-03   4100.5   <2e-16 ***
ORIGIN_GRID_ID1396          1.604e+01  5.987e-03   2679.8   <2e-16 ***
ORIGIN_GRID_ID1397          1.647e+01  2.882e-03   5715.1   <2e-16 ***
ORIGIN_GRID_ID1401          1.755e+01  2.059e-03   8524.6   <2e-16 ***
ORIGIN_GRID_ID1402          1.815e+01  1.674e-03  10838.5   <2e-16 ***
ORIGIN_GRID_ID1423          1.838e+01  5.963e-03   3083.1   <2e-16 ***
ORIGIN_GRID_ID1428          1.767e+01  1.991e-03   8873.7   <2e-16 ***
ORIGIN_GRID_ID1429          1.718e+01  3.215e-03   5342.9   <2e-16 ***
ORIGIN_GRID_ID1455          1.652e+01  2.743e-03   6023.0   <2e-16 ***
ORIGIN_GRID_ID1456          1.776e+01  1.773e-03  10019.8   <2e-16 ***
ORIGIN_GRID_ID1471          1.722e+01  2.131e-03   8078.5   <2e-16 ***
ORIGIN_GRID_ID1482          1.735e+01  1.925e-03   9013.2   <2e-16 ***
ORIGIN_GRID_ID1499          1.722e+01  2.104e-03   8186.4   <2e-16 ***
ORIGIN_GRID_ID1509          1.673e+01  3.494e-03   4789.2   <2e-16 ***
ORIGIN_GRID_ID1510          1.837e+01  1.568e-03  11714.5   <2e-16 ***
ORIGIN_GRID_ID1525          1.670e+01  2.227e-03   7501.8   <2e-16 ***
ORIGIN_GRID_ID1536          1.720e+01  1.835e-03   9375.6   <2e-16 ***
ORIGIN_GRID_ID1537          1.681e+01  3.660e-03   4592.8   <2e-16 ***
ORIGIN_GRID_ID1552          1.352e+01  1.426e-02    947.8   <2e-16 ***
ORIGIN_GRID_ID1553          1.595e+01  2.980e-03   5352.7   <2e-16 ***
ORIGIN_GRID_ID1563          1.687e+01  3.249e-03   5191.7   <2e-16 ***
ORIGIN_GRID_ID1564          1.828e+01  1.553e-03  11776.6   <2e-16 ***
ORIGIN_GRID_ID1578          1.490e+01  7.181e-03   2075.5   <2e-16 ***
ORIGIN_GRID_ID1579          1.722e+01  2.112e-03   8153.4   <2e-16 ***
ORIGIN_GRID_ID1590          1.802e+01  1.634e-03  11028.6   <2e-16 ***
ORIGIN_GRID_ID1591          1.833e+01  1.702e-03  10770.7   <2e-16 ***
ORIGIN_GRID_ID1605          1.624e+01  2.806e-03   5785.9   <2e-16 ***
ORIGIN_GRID_ID1606          1.624e+01  2.770e-03   5860.5   <2e-16 ***
ORIGIN_GRID_ID1617          1.629e+01  5.780e-03   2818.0   <2e-16 ***
ORIGIN_GRID_ID1618          1.800e+01  1.739e-03  10348.3   <2e-16 ***
ORIGIN_GRID_ID1631          1.537e+01  5.166e-03   2975.7   <2e-16 ***
ORIGIN_GRID_ID1632          1.680e+01  2.190e-03   7673.0   <2e-16 ***
ORIGIN_GRID_ID1634          1.660e+01  3.714e-03   4471.0   <2e-16 ***
ORIGIN_GRID_ID1644          1.687e+01  2.590e-03   6514.7   <2e-16 ***
ORIGIN_GRID_ID1645          1.810e+01  1.740e-03  10401.9   <2e-16 ***
ORIGIN_GRID_ID1658          1.734e+01  2.278e-03   7613.5   <2e-16 ***
ORIGIN_GRID_ID1659          1.670e+01  2.191e-03   7622.0   <2e-16 ***
ORIGIN_GRID_ID1672          1.692e+01  3.380e-03   5007.6   <2e-16 ***
ORIGIN_GRID_ID1684          1.687e+01  2.530e-03   6668.5   <2e-16 ***
ORIGIN_GRID_ID1685          1.605e+01  3.543e-03   4531.8   <2e-16 ***
ORIGIN_GRID_ID1686          1.661e+01  2.334e-03   7116.7   <2e-16 ***
ORIGIN_GRID_ID1688          1.420e+01  1.649e-02    860.6   <2e-16 ***
ORIGIN_GRID_ID1699          1.635e+01  2.658e-03   6149.4   <2e-16 ***
ORIGIN_GRID_ID1700          1.417e+01  2.247e-02    630.6   <2e-16 ***
ORIGIN_GRID_ID1712          1.604e+01  3.563e-03   4500.9   <2e-16 ***
ORIGIN_GRID_ID1713          1.731e+01  1.771e-03   9777.9   <2e-16 ***
ORIGIN_GRID_ID1727          1.835e+01  1.551e-03  11832.7   <2e-16 ***
ORIGIN_GRID_ID1739          1.653e+01  2.217e-03   7457.2   <2e-16 ***
ORIGIN_GRID_ID1753          1.798e+01  1.693e-03  10618.9   <2e-16 ***
ORIGIN_GRID_ID1754          1.725e+01  2.645e-03   6520.2   <2e-16 ***
ORIGIN_GRID_ID1766          1.762e+01  1.736e-03  10150.4   <2e-16 ***
ORIGIN_GRID_ID1767          1.696e+01  1.769e-03   9586.6   <2e-16 ***
ORIGIN_GRID_ID1780          1.535e+01  5.804e-03   2645.2   <2e-16 ***
ORIGIN_GRID_ID1781          1.720e+01  1.854e-03   9273.8   <2e-16 ***
ORIGIN_GRID_ID1792          1.653e+01  2.539e-03   6510.0   <2e-16 ***
ORIGIN_GRID_ID1793          1.718e+01  1.733e-03   9914.0   <2e-16 ***
ORIGIN_GRID_ID1794          1.570e+01  3.637e-03   4316.1   <2e-16 ***
ORIGIN_GRID_ID1807          1.677e+01  2.128e-03   7880.5   <2e-16 ***
ORIGIN_GRID_ID1820          1.645e+01  2.636e-03   6239.8   <2e-16 ***
ORIGIN_GRID_ID1821          1.774e+01  1.627e-03  10905.3   <2e-16 ***
ORIGIN_GRID_ID1833          1.764e+01  1.618e-03  10901.7   <2e-16 ***
ORIGIN_GRID_ID1835          1.721e+01  2.414e-03   7126.8   <2e-16 ***
ORIGIN_GRID_ID1847          1.675e+01  3.839e-03   4362.3   <2e-16 ***
ORIGIN_GRID_ID1854          1.574e+01  5.680e-03   2771.7   <2e-16 ***
ORIGIN_GRID_ID1859          1.661e+01  1.899e-03   8747.4   <2e-16 ***
ORIGIN_GRID_ID1860          1.706e+01  1.812e-03   9413.2   <2e-16 ***
ORIGIN_GRID_ID1861          1.776e+01  2.000e-03   8880.5   <2e-16 ***
ORIGIN_GRID_ID1874          1.616e+01  2.892e-03   5588.5   <2e-16 ***
ORIGIN_GRID_ID1875          1.653e+01  2.030e-03   8140.8   <2e-16 ***
ORIGIN_GRID_ID1882          1.711e+01  2.042e-03   8381.8   <2e-16 ***
ORIGIN_GRID_ID1883          1.653e+01  3.324e-03   4972.6   <2e-16 ***
ORIGIN_GRID_ID1886          1.781e+01  1.718e-03  10363.0   <2e-16 ***
ORIGIN_GRID_ID1887          1.764e+01  1.654e-03  10663.8   <2e-16 ***
ORIGIN_GRID_ID1888          1.685e+01  2.607e-03   6461.5   <2e-16 ***
ORIGIN_GRID_ID1905          1.506e+01  4.630e-03   3252.9   <2e-16 ***
ORIGIN_GRID_ID1907          1.659e+01  2.673e-03   6205.7   <2e-16 ***
ORIGIN_GRID_ID1908          1.596e+01  3.485e-03   4580.8   <2e-16 ***
ORIGIN_GRID_ID1909          1.719e+01  1.854e-03   9272.4   <2e-16 ***
ORIGIN_GRID_ID1912          1.521e+01  8.549e-03   1779.0   <2e-16 ***
ORIGIN_GRID_ID1913          1.651e+01  2.254e-03   7325.5   <2e-16 ***
ORIGIN_GRID_ID1914          1.815e+01  1.609e-03  11278.7   <2e-16 ***
ORIGIN_GRID_ID1928          1.536e+01  2.983e-03   5148.6   <2e-16 ***
ORIGIN_GRID_ID1929          1.524e+01  4.122e-03   3697.8   <2e-16 ***
ORIGIN_GRID_ID1933          1.623e+01  2.964e-03   5473.4   <2e-16 ***
ORIGIN_GRID_ID1935          1.667e+01  2.580e-03   6462.1   <2e-16 ***
ORIGIN_GRID_ID1936          1.705e+01  2.078e-03   8205.0   <2e-16 ***
ORIGIN_GRID_ID1937          1.640e+01  2.799e-03   5857.9   <2e-16 ***
ORIGIN_GRID_ID1940          1.720e+01  2.231e-03   7710.0   <2e-16 ***
ORIGIN_GRID_ID1941          1.724e+01  1.943e-03   8872.4   <2e-16 ***
ORIGIN_GRID_ID1942          1.683e+01  4.272e-03   3940.9   <2e-16 ***
ORIGIN_GRID_ID1955          1.707e+01  2.035e-03   8386.4   <2e-16 ***
ORIGIN_GRID_ID1959          1.678e+01  1.997e-03   8406.6   <2e-16 ***
ORIGIN_GRID_ID1960          1.710e+01  1.871e-03   9141.8   <2e-16 ***
ORIGIN_GRID_ID1962          1.685e+01  2.152e-03   7826.4   <2e-16 ***
ORIGIN_GRID_ID1963          1.609e+01  2.360e-03   6819.6   <2e-16 ***
ORIGIN_GRID_ID1967          1.838e+01  1.628e-03  11287.9   <2e-16 ***
ORIGIN_GRID_ID1968          1.853e+01  1.745e-03  10615.1   <2e-16 ***
ORIGIN_GRID_ID1985          1.532e+01  3.243e-03   4723.9   <2e-16 ***
ORIGIN_GRID_ID1987          1.754e+01  1.620e-03  10831.9   <2e-16 ***
ORIGIN_GRID_ID1988          1.610e+01  2.546e-03   6322.5   <2e-16 ***
ORIGIN_GRID_ID1989          1.636e+01  2.605e-03   6279.5   <2e-16 ***
ORIGIN_GRID_ID1990          1.807e+01  1.559e-03  11590.2   <2e-16 ***
ORIGIN_GRID_ID1994          1.646e+01  5.302e-03   3103.6   <2e-16 ***
ORIGIN_GRID_ID1995          1.865e+01  1.639e-03  11382.5   <2e-16 ***
ORIGIN_GRID_ID2010          1.534e+01  2.516e-03   6099.0   <2e-16 ***
ORIGIN_GRID_ID2011          1.640e+01  1.809e-03   9067.9   <2e-16 ***
ORIGIN_GRID_ID2012          1.549e+01  3.826e-03   4048.4   <2e-16 ***
ORIGIN_GRID_ID2013          1.637e+01  2.209e-03   7410.4   <2e-16 ***
ORIGIN_GRID_ID2014          1.669e+01  2.013e-03   8291.7   <2e-16 ***
ORIGIN_GRID_ID2015          1.670e+01  2.843e-03   5874.5   <2e-16 ***
ORIGIN_GRID_ID2016          1.689e+01  2.051e-03   8234.5   <2e-16 ***
ORIGIN_GRID_ID2017          1.688e+01  2.066e-03   8171.5   <2e-16 ***
ORIGIN_GRID_ID2021          1.680e+01  3.456e-03   4860.6   <2e-16 ***
ORIGIN_GRID_ID2038          1.564e+01  1.870e-03   8361.5   <2e-16 ***
ORIGIN_GRID_ID2039          1.714e+01  2.291e-03   7480.1   <2e-16 ***
ORIGIN_GRID_ID2040          1.731e+01  1.746e-03   9915.5   <2e-16 ***
ORIGIN_GRID_ID2041          1.818e+01  1.584e-03  11477.7   <2e-16 ***
ORIGIN_GRID_ID2042          1.667e+01  2.558e-03   6516.3   <2e-16 ***
ORIGIN_GRID_ID2043          1.541e+01  4.986e-03   3091.2   <2e-16 ***
ORIGIN_GRID_ID2044          1.789e+01  1.605e-03  11147.3   <2e-16 ***
ORIGIN_GRID_ID2064          1.330e+01  8.910e-03   1492.8   <2e-16 ***
ORIGIN_GRID_ID2065          1.556e+01  2.483e-03   6265.7   <2e-16 ***
ORIGIN_GRID_ID2066          1.590e+01  2.491e-03   6381.0   <2e-16 ***
ORIGIN_GRID_ID2067          1.721e+01  2.177e-03   7903.9   <2e-16 ***
ORIGIN_GRID_ID2068          1.729e+01  2.150e-03   8041.0   <2e-16 ***
ORIGIN_GRID_ID2070          1.739e+01  2.310e-03   7529.8   <2e-16 ***
ORIGIN_GRID_ID2071          1.675e+01  2.988e-03   5606.3   <2e-16 ***
ORIGIN_GRID_ID2093          1.586e+01  2.038e-03   7780.9   <2e-16 ***
ORIGIN_GRID_ID2094          1.700e+01  2.314e-03   7346.8   <2e-16 ***
ORIGIN_GRID_ID2095          1.765e+01  2.736e-03   6450.4   <2e-16 ***
ORIGIN_GRID_ID2098          1.589e+01  4.140e-03   3838.0   <2e-16 ***
ORIGIN_GRID_ID2119          1.629e+01  2.404e-03   6779.1   <2e-16 ***
ORIGIN_GRID_ID2120          1.602e+01  2.700e-03   5933.7   <2e-16 ***
ORIGIN_GRID_ID2123          1.655e+01  2.271e-03   7287.3   <2e-16 ***
ORIGIN_GRID_ID2147          1.641e+01  2.035e-03   8064.3   <2e-16 ***
ORIGIN_GRID_ID2148          1.739e+01  1.709e-03  10174.9   <2e-16 ***
ORIGIN_GRID_ID2149          1.656e+01  2.802e-03   5912.1   <2e-16 ***
ORIGIN_GRID_ID2150          1.523e+01  4.185e-03   3638.8   <2e-16 ***
ORIGIN_GRID_ID2151          1.621e+01  2.691e-03   6025.2   <2e-16 ***
ORIGIN_GRID_ID2152          1.712e+01  2.404e-03   7120.2   <2e-16 ***
ORIGIN_GRID_ID2154          1.652e+01  3.033e-03   5447.7   <2e-16 ***
ORIGIN_GRID_ID2174          1.587e+01  3.764e-03   4217.3   <2e-16 ***
ORIGIN_GRID_ID2177          1.786e+01  1.629e-03  10961.8   <2e-16 ***
ORIGIN_GRID_ID2178          1.697e+01  1.875e-03   9055.6   <2e-16 ***
ORIGIN_GRID_ID2179          1.729e+01  2.120e-03   8155.7   <2e-16 ***
ORIGIN_GRID_ID2180          1.706e+01  2.575e-03   6624.2   <2e-16 ***
ORIGIN_GRID_ID2201          1.702e+01  1.936e-03   8789.2   <2e-16 ***
ORIGIN_GRID_ID2203          1.677e+01  3.262e-03   5143.0   <2e-16 ***
ORIGIN_GRID_ID2204          1.574e+01  3.336e-03   4716.7   <2e-16 ***
ORIGIN_GRID_ID2205          1.625e+01  2.091e-03   7769.7   <2e-16 ***
ORIGIN_GRID_ID2206          1.822e+01  1.583e-03  11516.0   <2e-16 ***
ORIGIN_GRID_ID2208          1.768e+01  2.059e-03   8590.0   <2e-16 ***
ORIGIN_GRID_ID2228          1.657e+01  2.223e-03   7453.3   <2e-16 ***
ORIGIN_GRID_ID2231          1.664e+01  2.058e-03   8085.6   <2e-16 ***
ORIGIN_GRID_ID2233          1.821e+01  1.586e-03  11480.7   <2e-16 ***
ORIGIN_GRID_ID2234          1.453e+01  2.494e-02    582.6   <2e-16 ***
ORIGIN_GRID_ID2235          1.434e+01  2.054e-02    698.0   <2e-16 ***
ORIGIN_GRID_ID2254          1.544e+01  7.921e-03   1949.2   <2e-16 ***
ORIGIN_GRID_ID2255          1.682e+01  2.289e-03   7346.9   <2e-16 ***
ORIGIN_GRID_ID2256          1.647e+01  2.350e-03   7008.3   <2e-16 ***
ORIGIN_GRID_ID2257          1.522e+01  1.229e-02   1238.7   <2e-16 ***
ORIGIN_GRID_ID2259          1.544e+01  5.622e-03   2746.4   <2e-16 ***
ORIGIN_GRID_ID2260          1.771e+01  1.755e-03  10088.9   <2e-16 ***
ORIGIN_GRID_ID2261          1.791e+01  1.696e-03  10562.9   <2e-16 ***
ORIGIN_GRID_ID2262          1.680e+01  2.816e-03   5967.7   <2e-16 ***
ORIGIN_GRID_ID2281          1.672e+01  3.003e-03   5566.0   <2e-16 ***
ORIGIN_GRID_ID2282          1.631e+01  2.711e-03   6013.6   <2e-16 ***
ORIGIN_GRID_ID2283          1.697e+01  1.920e-03   8838.4   <2e-16 ***
ORIGIN_GRID_ID2285          1.764e+01  1.770e-03   9963.0   <2e-16 ***
ORIGIN_GRID_ID2286          1.635e+01  2.817e-03   5801.6   <2e-16 ***
ORIGIN_GRID_ID2287          1.821e+01  1.564e-03  11637.2   <2e-16 ***
ORIGIN_GRID_ID2288          1.591e+01  4.613e-03   3449.7   <2e-16 ***
ORIGIN_GRID_ID2310          1.648e+01  2.241e-03   7352.8   <2e-16 ***
ORIGIN_GRID_ID2312          1.462e+01  1.063e-02   1375.6   <2e-16 ***
ORIGIN_GRID_ID2313          1.694e+01  1.943e-03   8720.5   <2e-16 ***
ORIGIN_GRID_ID2314          1.742e+01  1.605e-03  10854.0   <2e-16 ***
ORIGIN_GRID_ID2315          1.679e+01  2.163e-03   7761.0   <2e-16 ***
ORIGIN_GRID_ID2316          1.788e+01  1.559e-03  11466.6   <2e-16 ***
ORIGIN_GRID_ID2335          1.451e+01  1.078e-02   1345.3   <2e-16 ***
ORIGIN_GRID_ID2339          1.681e+01  2.605e-03   6453.6   <2e-16 ***
ORIGIN_GRID_ID2340          1.760e+01  1.690e-03  10412.6   <2e-16 ***
ORIGIN_GRID_ID2341          1.723e+01  1.749e-03   9856.6   <2e-16 ***
ORIGIN_GRID_ID2342          1.661e+01  1.907e-03   8708.0   <2e-16 ***
ORIGIN_GRID_ID2343          1.673e+01  2.416e-03   6925.7   <2e-16 ***
ORIGIN_GRID_ID2363          1.620e+01  3.378e-03   4796.0   <2e-16 ***
ORIGIN_GRID_ID2367          1.667e+01  2.787e-03   5981.5   <2e-16 ***
ORIGIN_GRID_ID2368          1.739e+01  1.872e-03   9289.0   <2e-16 ***
ORIGIN_GRID_ID2369          1.695e+01  2.118e-03   8004.5   <2e-16 ***
ORIGIN_GRID_ID2370          1.738e+01  1.702e-03  10210.7   <2e-16 ***
ORIGIN_GRID_ID2371          1.741e+01  1.812e-03   9610.8   <2e-16 ***
ORIGIN_GRID_ID2390          1.639e+01  2.762e-03   5933.7   <2e-16 ***
ORIGIN_GRID_ID2391          1.641e+01  2.537e-03   6467.9   <2e-16 ***
ORIGIN_GRID_ID2394          1.584e+01  4.468e-03   3545.7   <2e-16 ***
ORIGIN_GRID_ID2395          1.787e+01  1.706e-03  10475.2   <2e-16 ***
ORIGIN_GRID_ID2396          1.742e+01  1.632e-03  10677.0   <2e-16 ***
ORIGIN_GRID_ID2397          1.654e+01  2.443e-03   6771.5   <2e-16 ***
ORIGIN_GRID_ID2398          1.688e+01  2.465e-03   6847.7   <2e-16 ***
ORIGIN_GRID_ID2418          1.647e+01  3.090e-03   5331.0   <2e-16 ***
ORIGIN_GRID_ID2419          1.580e+01  4.073e-03   3878.2   <2e-16 ***
ORIGIN_GRID_ID2422          1.636e+01  6.285e-03   2603.4   <2e-16 ***
ORIGIN_GRID_ID2423          1.673e+01  2.553e-03   6554.3   <2e-16 ***
ORIGIN_GRID_ID2424          1.770e+01  1.581e-03  11193.1   <2e-16 ***
ORIGIN_GRID_ID2425          1.716e+01  1.840e-03   9329.2   <2e-16 ***
ORIGIN_GRID_ID2426          1.645e+01  3.722e-03   4419.2   <2e-16 ***
ORIGIN_GRID_ID2443          1.699e+01  2.218e-03   7660.4   <2e-16 ***
ORIGIN_GRID_ID2445          1.724e+01  1.839e-03   9375.6   <2e-16 ***
ORIGIN_GRID_ID2449          1.737e+01  3.075e-03   5650.3   <2e-16 ***
ORIGIN_GRID_ID2450          1.719e+01  1.995e-03   8615.7   <2e-16 ***
ORIGIN_GRID_ID2451          1.766e+01  1.657e-03  10657.3   <2e-16 ***
ORIGIN_GRID_ID2472          1.501e+01  1.801e-02    833.5   <2e-16 ***
ORIGIN_GRID_ID2473          1.703e+01  2.366e-03   7196.1   <2e-16 ***
ORIGIN_GRID_ID2478          1.679e+01  2.208e-03   7601.2   <2e-16 ***
ORIGIN_GRID_ID2479          1.552e+01  5.926e-03   2618.6   <2e-16 ***
ORIGIN_GRID_ID2497          1.726e+01  2.010e-03   8585.5   <2e-16 ***
ORIGIN_GRID_ID2499          1.753e+01  2.326e-03   7535.7   <2e-16 ***
ORIGIN_GRID_ID2505          1.693e+01  2.352e-03   7198.3   <2e-16 ***
ORIGIN_GRID_ID2527          1.737e+01  2.010e-03   8645.1   <2e-16 ***
ORIGIN_GRID_ID2532          1.697e+01  2.583e-03   6569.2   <2e-16 ***
ORIGIN_GRID_ID2533          1.724e+01  3.091e-03   5576.2   <2e-16 ***
ORIGIN_GRID_ID2551          1.672e+01  2.922e-03   5721.9   <2e-16 ***
ORIGIN_GRID_ID2553          1.685e+01  4.119e-03   4090.0   <2e-16 ***
ORIGIN_GRID_ID2554          1.554e+01  6.321e-03   2458.3   <2e-16 ***
ORIGIN_GRID_ID2559          1.697e+01  2.976e-03   5704.4   <2e-16 ***
ORIGIN_GRID_ID2580          1.740e+01  2.029e-03   8574.9   <2e-16 ***
ORIGIN_GRID_ID2581          1.664e+01  3.690e-03   4509.0   <2e-16 ***
ORIGIN_GRID_ID2607          1.796e+01  1.657e-03  10838.1   <2e-16 ***
ORIGIN_GRID_ID2608          1.631e+01  3.939e-03   4141.2   <2e-16 ***
ORIGIN_GRID_ID2634          1.777e+01  1.811e-03   9809.6   <2e-16 ***
ORIGIN_GRID_ID2635          1.787e+01  2.035e-03   8783.6   <2e-16 ***
ORIGIN_GRID_ID2636          1.732e+01  2.310e-03   7495.5   <2e-16 ***
ORIGIN_GRID_ID2661          1.732e+01  1.844e-03   9388.4   <2e-16 ***
ORIGIN_GRID_ID2663          1.794e+01  1.614e-03  11118.6   <2e-16 ***
ORIGIN_GRID_ID2665          1.699e+01  2.668e-03   6368.3   <2e-16 ***
ORIGIN_GRID_ID2688          1.736e+01  1.952e-03   8891.5   <2e-16 ***
ORIGIN_GRID_ID2689          1.737e+01  2.063e-03   8419.2   <2e-16 ***
ORIGIN_GRID_ID2690          1.639e+01  2.578e-03   6356.9   <2e-16 ***
ORIGIN_GRID_ID2691          1.807e+01  1.648e-03  10965.6   <2e-16 ***
ORIGIN_GRID_ID2693          1.770e+01  1.910e-03   9268.7   <2e-16 ***
ORIGIN_GRID_ID2715          1.786e+01  1.938e-03   9211.8   <2e-16 ***
ORIGIN_GRID_ID2717          1.666e+01  1.928e-03   8643.5   <2e-16 ***
ORIGIN_GRID_ID2718          1.714e+01  2.538e-03   6753.9   <2e-16 ***
ORIGIN_GRID_ID2719          1.798e+01  1.649e-03  10906.6   <2e-16 ***
ORIGIN_GRID_ID2742          1.715e+01  2.403e-03   7137.0   <2e-16 ***
ORIGIN_GRID_ID2743          1.613e+01  5.075e-03   3178.4   <2e-16 ***
ORIGIN_GRID_ID2744          1.694e+01  1.999e-03   8477.3   <2e-16 ***
ORIGIN_GRID_ID2745          1.689e+01  1.886e-03   8953.2   <2e-16 ***
ORIGIN_GRID_ID2747          1.690e+01  2.400e-03   7039.8   <2e-16 ***
ORIGIN_GRID_ID2768          1.748e+01  2.226e-03   7852.0   <2e-16 ***
ORIGIN_GRID_ID2771          1.763e+01  1.712e-03  10294.0   <2e-16 ***
ORIGIN_GRID_ID2773          1.723e+01  1.978e-03   8710.8   <2e-16 ***
ORIGIN_GRID_ID2798          1.639e+01  2.920e-03   5613.6   <2e-16 ***
ORIGIN_GRID_ID2799          1.714e+01  1.785e-03   9602.6   <2e-16 ***
ORIGIN_GRID_ID2800          1.719e+01  2.040e-03   8427.4   <2e-16 ***
ORIGIN_GRID_ID2824          1.642e+01  2.878e-03   5707.6   <2e-16 ***
ORIGIN_GRID_ID2825          1.720e+01  1.716e-03  10022.9   <2e-16 ***
ORIGIN_GRID_ID2826          1.731e+01  2.261e-03   7657.5   <2e-16 ***
ORIGIN_GRID_ID2827          1.751e+01  1.915e-03   9143.2   <2e-16 ***
ORIGIN_GRID_ID2852          1.740e+01  1.971e-03   8829.9   <2e-16 ***
ORIGIN_GRID_ID2853          1.738e+01  1.669e-03  10412.4   <2e-16 ***
ORIGIN_GRID_ID2854          1.787e+01  1.713e-03  10431.5   <2e-16 ***
ORIGIN_GRID_ID2878          1.676e+01  2.782e-03   6023.3   <2e-16 ***
ORIGIN_GRID_ID2879          1.712e+01  2.044e-03   8378.9   <2e-16 ***
ORIGIN_GRID_ID2880          1.711e+01  2.058e-03   8315.0   <2e-16 ***
ORIGIN_GRID_ID2881          1.837e+01  1.750e-03  10499.6   <2e-16 ***
ORIGIN_GRID_ID2907          1.716e+01  2.399e-03   7151.5   <2e-16 ***
ORIGIN_GRID_ID2908          1.759e+01  2.007e-03   8761.8   <2e-16 ***
ORIGIN_GRID_ID2933          1.530e+01  7.912e-03   1934.0   <2e-16 ***
ORIGIN_GRID_ID2934          1.686e+01  2.563e-03   6579.5   <2e-16 ***
ORIGIN_GRID_ID3098          1.660e+01  5.416e-03   3064.1   <2e-16 ***
log(TDESTIN_BIZ_COUNT)      2.678e-02  1.005e-04    266.4   <2e-16 ***
log(TDESTIN_FINSERV_COUNT)  2.693e-01  9.400e-05   2864.9   <2e-16 ***
log(TDESTIN_MRTEXIT_COUNT)  6.207e-01  1.500e-04   4136.9   <2e-16 ***
log(TDESTIN_BUSSTOP_COUNT)  1.294e-01  2.503e-04    517.0   <2e-16 ***
log(TDESTIN_HDBCOMM_UNITS)  3.644e-02  6.003e-05    607.1   <2e-16 ***
log(TDESTIN_HDBRES_UNITS)  -2.590e-02  1.391e-04   -186.2   <2e-16 ***
log(TDESTIN_SCHOOLS_COUNT)  3.070e-01  2.282e-04   1345.1   <2e-16 ***
log(DISTANCE)              -1.466e+00  1.266e-04 -11575.0   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2876477793  on 101668  degrees of freedom
Residual deviance:  149532408  on 101312  degrees of freedom
AIC: 150290729

Number of Fisher Scoring iterations: 6
CalcRSquared(orcSIM_Poisson4$data$TRIPS, orcSIM_Poisson4$fitted.values)
[1] 0.6215009
decSIM_Poisson4 <- glm(formula = TRIPS ~ 
                DESTIN_GRID_ID +
                log(TORIGIN_BIZ_COUNT) +
                log(TORIGIN_FINSERV_COUNT) +
                  log(TORIGIN_MRTEXIT_COUNT) +
                  log(TORIGIN_BUSSTOP_COUNT) +
                  log(TORIGIN_HDBCOMM_UNITS) +
                  log(TORIGIN_HDBRES_UNITS) + 
                  log(TORIGIN_SCHOOLS_COUNT) + 
                log(DISTANCE) - 1,
              family = poisson(link = "log"),
              data = inter_zonal_flow1,
              na.action = na.exclude)
summary(decSIM_Poisson4)

Call:
glm(formula = TRIPS ~ DESTIN_GRID_ID + log(TORIGIN_BIZ_COUNT) + 
    log(TORIGIN_FINSERV_COUNT) + log(TORIGIN_MRTEXIT_COUNT) + 
    log(TORIGIN_BUSSTOP_COUNT) + log(TORIGIN_HDBCOMM_UNITS) + 
    log(TORIGIN_HDBRES_UNITS) + log(TORIGIN_SCHOOLS_COUNT) + 
    log(DISTANCE) - 1, family = poisson(link = "log"), data = inter_zonal_flow1, 
    na.action = na.exclude)

Coefficients:
                             Estimate Std. Error    z value Pr(>|z|)    
DESTIN_GRID_ID664           1.411e+01  4.596e-03   3069.630  < 2e-16 ***
DESTIN_GRID_ID718           1.393e+01  1.976e-03   7050.301  < 2e-16 ***
DESTIN_GRID_ID745           1.234e+01  3.086e-03   3999.637  < 2e-16 ***
DESTIN_GRID_ID746           1.320e+01  2.390e-03   5524.947  < 2e-16 ***
DESTIN_GRID_ID772           1.440e+01  1.631e-03   8824.931  < 2e-16 ***
DESTIN_GRID_ID799           1.446e+01  1.853e-03   7802.283  < 2e-16 ***
DESTIN_GRID_ID800           1.328e+01  1.959e-03   6779.892  < 2e-16 ***
DESTIN_GRID_ID826           1.525e+01  1.614e-03   9445.913  < 2e-16 ***
DESTIN_GRID_ID827           1.417e+01  2.154e-03   6577.737  < 2e-16 ***
DESTIN_GRID_ID854           1.297e+01  2.599e-03   4991.964  < 2e-16 ***
DESTIN_GRID_ID880           1.242e+01  3.595e-03   3455.464  < 2e-16 ***
DESTIN_GRID_ID881           1.299e+01  3.612e-03   3596.857  < 2e-16 ***
DESTIN_GRID_ID908           1.337e+01  2.126e-03   6287.073  < 2e-16 ***
DESTIN_GRID_ID934           1.373e+01  2.039e-03   6733.251  < 2e-16 ***
DESTIN_GRID_ID935           1.339e+01  2.287e-03   5854.102  < 2e-16 ***
DESTIN_GRID_ID961           1.327e+01  2.500e-03   5307.049  < 2e-16 ***
DESTIN_GRID_ID962           1.536e+01  1.575e-03   9754.991  < 2e-16 ***
DESTIN_GRID_ID987           1.434e+01  1.835e-03   7813.299  < 2e-16 ***
DESTIN_GRID_ID988           1.240e+01  3.427e-03   3619.030  < 2e-16 ***
DESTIN_GRID_ID989           1.354e+01  2.131e-03   6353.711  < 2e-16 ***
DESTIN_GRID_ID1015          1.109e+01  8.499e-03   1304.500  < 2e-16 ***
DESTIN_GRID_ID1016          1.269e+01  2.660e-03   4771.515  < 2e-16 ***
DESTIN_GRID_ID1043          1.332e+01  3.087e-03   4314.896  < 2e-16 ***
DESTIN_GRID_ID1068          1.138e+01  2.065e-02    551.035  < 2e-16 ***
DESTIN_GRID_ID1070          1.362e+01  2.000e-03   6808.228  < 2e-16 ***
DESTIN_GRID_ID1096          1.319e+01  2.160e-03   6106.978  < 2e-16 ***
DESTIN_GRID_ID1097          1.282e+01  2.999e-03   4273.618  < 2e-16 ***
DESTIN_GRID_ID1099          1.349e+01  2.147e-03   6284.002  < 2e-16 ***
DESTIN_GRID_ID1122          1.392e+01  2.472e-03   5630.029  < 2e-16 ***
DESTIN_GRID_ID1123          1.493e+01  1.621e-03   9210.705  < 2e-16 ***
DESTIN_GRID_ID1124          1.349e+01  2.147e-03   6281.108  < 2e-16 ***
DESTIN_GRID_ID1125          1.280e+01  2.976e-03   4302.060  < 2e-16 ***
DESTIN_GRID_ID1127          1.302e+01  2.348e-03   5546.149  < 2e-16 ***
DESTIN_GRID_ID1128          1.370e+01  2.745e-03   4991.138  < 2e-16 ***
DESTIN_GRID_ID1148          1.309e+01  3.192e-03   4102.538  < 2e-16 ***
DESTIN_GRID_ID1150          1.353e+01  2.049e-03   6605.560  < 2e-16 ***
DESTIN_GRID_ID1151          1.300e+01  2.360e-03   5506.781  < 2e-16 ***
DESTIN_GRID_ID1152          1.270e+01  3.522e-03   3606.952  < 2e-16 ***
DESTIN_GRID_ID1153          1.341e+01  2.219e-03   6044.397  < 2e-16 ***
DESTIN_GRID_ID1154          1.507e+01  1.646e-03   9156.771  < 2e-16 ***
DESTIN_GRID_ID1155          1.042e+01  1.727e-02    603.087  < 2e-16 ***
DESTIN_GRID_ID1176          1.401e+01  2.035e-03   6884.083  < 2e-16 ***
DESTIN_GRID_ID1178          1.292e+01  2.270e-03   5691.640  < 2e-16 ***
DESTIN_GRID_ID1179          1.217e+01  3.325e-03   3659.796  < 2e-16 ***
DESTIN_GRID_ID1180          1.063e+01  1.021e-02   1041.383  < 2e-16 ***
DESTIN_GRID_ID1181          1.376e+01  1.863e-03   7384.959  < 2e-16 ***
DESTIN_GRID_ID1182          1.327e+01  2.359e-03   5625.747  < 2e-16 ***
DESTIN_GRID_ID1183          1.315e+01  5.061e-03   2598.262  < 2e-16 ***
DESTIN_GRID_ID1205          1.455e+01  1.657e-03   8782.855  < 2e-16 ***
DESTIN_GRID_ID1206          1.335e+01  2.357e-03   5666.434  < 2e-16 ***
DESTIN_GRID_ID1207          1.317e+01  2.539e-03   5186.290  < 2e-16 ***
DESTIN_GRID_ID1209          1.482e+01  1.786e-03   8297.218  < 2e-16 ***
DESTIN_GRID_ID1232          1.376e+01  1.926e-03   7145.403  < 2e-16 ***
DESTIN_GRID_ID1233          1.438e+01  2.242e-03   6414.371  < 2e-16 ***
DESTIN_GRID_ID1235          1.412e+01  2.001e-03   7057.737  < 2e-16 ***
DESTIN_GRID_ID1255          1.414e+01  5.672e-03   2492.787  < 2e-16 ***
DESTIN_GRID_ID1258          1.448e+01  2.027e-03   7146.249  < 2e-16 ***
DESTIN_GRID_ID1259          1.300e+01  2.757e-03   4715.937  < 2e-16 ***
DESTIN_GRID_ID1261          1.289e+01  2.537e-03   5080.590  < 2e-16 ***
DESTIN_GRID_ID1262          1.337e+01  2.191e-03   6101.903  < 2e-16 ***
DESTIN_GRID_ID1283          1.312e+01  2.789e-03   4704.539  < 2e-16 ***
DESTIN_GRID_ID1284          1.270e+01  4.688e-03   2709.861  < 2e-16 ***
DESTIN_GRID_ID1286          1.209e+01  4.576e-03   2642.245  < 2e-16 ***
DESTIN_GRID_ID1289          1.385e+01  1.782e-03   7769.743  < 2e-16 ***
DESTIN_GRID_ID1309          1.429e+01  2.172e-03   6580.531  < 2e-16 ***
DESTIN_GRID_ID1310          1.497e+01  1.636e-03   9150.318  < 2e-16 ***
DESTIN_GRID_ID1315          1.460e+01  1.675e-03   8714.463  < 2e-16 ***
DESTIN_GRID_ID1316          1.235e+01  3.723e-03   3317.462  < 2e-16 ***
DESTIN_GRID_ID1337          1.328e+01  2.184e-03   6078.320  < 2e-16 ***
DESTIN_GRID_ID1338          1.253e+01  5.832e-03   2147.658  < 2e-16 ***
DESTIN_GRID_ID1343          1.238e+01  2.944e-03   4204.260  < 2e-16 ***
DESTIN_GRID_ID1363          1.405e+01  2.496e-03   5630.967  < 2e-16 ***
DESTIN_GRID_ID1364          1.283e+01  3.012e-03   4260.794  < 2e-16 ***
DESTIN_GRID_ID1366          1.326e+01  2.886e-03   4595.010  < 2e-16 ***
DESTIN_GRID_ID1369          1.345e+01  2.198e-03   6118.225  < 2e-16 ***
DESTIN_GRID_ID1370          1.328e+01  2.427e-03   5473.693  < 2e-16 ***
DESTIN_GRID_ID1374          1.266e+01  3.243e-03   3903.289  < 2e-16 ***
DESTIN_GRID_ID1375          1.304e+01  5.625e-03   2317.928  < 2e-16 ***
DESTIN_GRID_ID1391          1.292e+01  4.010e-03   3222.446  < 2e-16 ***
DESTIN_GRID_ID1392          1.180e+01  6.546e-03   1803.172  < 2e-16 ***
DESTIN_GRID_ID1396          1.172e+01  8.298e-03   1412.510  < 2e-16 ***
DESTIN_GRID_ID1397          1.291e+01  2.669e-03   4835.587  < 2e-16 ***
DESTIN_GRID_ID1401          1.449e+01  1.866e-03   7764.771  < 2e-16 ***
DESTIN_GRID_ID1402          1.355e+01  2.154e-03   6291.867  < 2e-16 ***
DESTIN_GRID_ID1423          1.300e+01  4.294e-03   3028.269  < 2e-16 ***
DESTIN_GRID_ID1428          1.296e+01  2.708e-03   4786.784  < 2e-16 ***
DESTIN_GRID_ID1429          1.360e+01  2.895e-03   4699.371  < 2e-16 ***
DESTIN_GRID_ID1455          1.284e+01  2.758e-03   4653.229  < 2e-16 ***
DESTIN_GRID_ID1456          1.308e+01  2.553e-03   5125.604  < 2e-16 ***
DESTIN_GRID_ID1471          1.351e+01  2.980e-03   4534.504  < 2e-16 ***
DESTIN_GRID_ID1482          1.446e+01  1.783e-03   8105.722  < 2e-16 ***
DESTIN_GRID_ID1499          1.268e+01  4.673e-03   2714.387  < 2e-16 ***
DESTIN_GRID_ID1509          1.234e+01  4.745e-03   2600.976  < 2e-16 ***
DESTIN_GRID_ID1510          1.526e+01  1.601e-03   9526.597  < 2e-16 ***
DESTIN_GRID_ID1525          1.403e+01  1.905e-03   7365.747  < 2e-16 ***
DESTIN_GRID_ID1536          1.381e+01  1.854e-03   7447.753  < 2e-16 ***
DESTIN_GRID_ID1537          1.391e+01  2.738e-03   5080.645  < 2e-16 ***
DESTIN_GRID_ID1552          1.151e+01  9.412e-03   1223.267  < 2e-16 ***
DESTIN_GRID_ID1553          1.294e+01  3.214e-03   4025.075  < 2e-16 ***
DESTIN_GRID_ID1563          1.361e+01  2.446e-03   5563.871  < 2e-16 ***
DESTIN_GRID_ID1564          1.364e+01  1.856e-03   7349.062  < 2e-16 ***
DESTIN_GRID_ID1578          1.164e+01  6.338e-03   1836.810  < 2e-16 ***
DESTIN_GRID_ID1579          1.379e+01  2.160e-03   6384.075  < 2e-16 ***
DESTIN_GRID_ID1590          1.335e+01  2.142e-03   6233.518  < 2e-16 ***
DESTIN_GRID_ID1591          1.378e+01  2.131e-03   6467.685  < 2e-16 ***
DESTIN_GRID_ID1605          1.324e+01  2.503e-03   5290.048  < 2e-16 ***
DESTIN_GRID_ID1606          1.320e+01  2.577e-03   5123.418  < 2e-16 ***
DESTIN_GRID_ID1617          1.217e+01  6.541e-03   1860.682  < 2e-16 ***
DESTIN_GRID_ID1618          1.516e+01  1.624e-03   9339.322  < 2e-16 ***
DESTIN_GRID_ID1631          1.286e+01  3.196e-03   4022.076  < 2e-16 ***
DESTIN_GRID_ID1632          1.296e+01  2.667e-03   4858.398  < 2e-16 ***
DESTIN_GRID_ID1634          1.293e+01  4.426e-03   2920.649  < 2e-16 ***
DESTIN_GRID_ID1644          1.343e+01  2.461e-03   5458.130  < 2e-16 ***
DESTIN_GRID_ID1645          1.388e+01  2.052e-03   6764.451  < 2e-16 ***
DESTIN_GRID_ID1658          1.277e+01  3.320e-03   3845.619  < 2e-16 ***
DESTIN_GRID_ID1659          1.352e+01  2.030e-03   6658.629  < 2e-16 ***
DESTIN_GRID_ID1672          1.336e+01  3.541e-03   3772.202  < 2e-16 ***
DESTIN_GRID_ID1684          1.343e+01  2.444e-03   5495.499  < 2e-16 ***
DESTIN_GRID_ID1685          1.314e+01  3.442e-03   3817.795  < 2e-16 ***
DESTIN_GRID_ID1686          1.316e+01  2.488e-03   5291.254  < 2e-16 ***
DESTIN_GRID_ID1688          1.260e+01  5.944e-03   2120.298  < 2e-16 ***
DESTIN_GRID_ID1699          1.351e+01  2.212e-03   6108.636  < 2e-16 ***
DESTIN_GRID_ID1700          1.306e+01  5.999e-03   2177.781  < 2e-16 ***
DESTIN_GRID_ID1712          1.207e+01  3.983e-03   3031.588  < 2e-16 ***
DESTIN_GRID_ID1713          1.389e+01  1.842e-03   7542.344  < 2e-16 ***
DESTIN_GRID_ID1727          1.370e+01  2.013e-03   6808.929  < 2e-16 ***
DESTIN_GRID_ID1739          1.401e+01  1.760e-03   7959.467  < 2e-16 ***
DESTIN_GRID_ID1753          1.503e+01  1.592e-03   9443.417  < 2e-16 ***
DESTIN_GRID_ID1754          1.319e+01  2.753e-03   4791.551  < 2e-16 ***
DESTIN_GRID_ID1766          1.346e+01  2.003e-03   6720.958  < 2e-16 ***
DESTIN_GRID_ID1767          1.345e+01  1.938e-03   6941.139  < 2e-16 ***
DESTIN_GRID_ID1780          1.290e+01  1.006e-02   1282.768  < 2e-16 ***
DESTIN_GRID_ID1781          1.322e+01  2.385e-03   5541.707  < 2e-16 ***
DESTIN_GRID_ID1792          1.255e+01  3.061e-03   4100.792  < 2e-16 ***
DESTIN_GRID_ID1793          1.372e+01  1.858e-03   7388.149  < 2e-16 ***
DESTIN_GRID_ID1794          1.265e+01  3.569e-03   3543.418  < 2e-16 ***
DESTIN_GRID_ID1807          1.201e+01  3.416e-03   3515.530  < 2e-16 ***
DESTIN_GRID_ID1820          1.288e+01  2.780e-03   4632.733  < 2e-16 ***
DESTIN_GRID_ID1821          1.442e+01  1.702e-03   8472.701  < 2e-16 ***
DESTIN_GRID_ID1833          1.398e+01  1.765e-03   7916.872  < 2e-16 ***
DESTIN_GRID_ID1835          1.234e+01  3.639e-03   3389.950  < 2e-16 ***
DESTIN_GRID_ID1847          1.166e+01  9.244e-03   1261.836  < 2e-16 ***
DESTIN_GRID_ID1854          1.300e+01  3.548e-03   3664.431  < 2e-16 ***
DESTIN_GRID_ID1859          1.277e+01  2.202e-03   5799.728  < 2e-16 ***
DESTIN_GRID_ID1860          1.301e+01  2.283e-03   5698.485  < 2e-16 ***
DESTIN_GRID_ID1861          1.275e+01  3.488e-03   3654.776  < 2e-16 ***
DESTIN_GRID_ID1874          1.321e+01  2.445e-03   5404.812  < 2e-16 ***
DESTIN_GRID_ID1875          1.359e+01  1.967e-03   6906.887  < 2e-16 ***
DESTIN_GRID_ID1882          1.382e+01  2.036e-03   6788.004  < 2e-16 ***
DESTIN_GRID_ID1883          1.241e+01  3.781e-03   3282.010  < 2e-16 ***
DESTIN_GRID_ID1886          1.496e+01  1.655e-03   9038.184  < 2e-16 ***
DESTIN_GRID_ID1887          1.511e+01  1.561e-03   9680.416  < 2e-16 ***
DESTIN_GRID_ID1888          1.285e+01  3.492e-03   3680.293  < 2e-16 ***
DESTIN_GRID_ID1905          1.236e+01  3.955e-03   3124.821  < 2e-16 ***
DESTIN_GRID_ID1907          1.328e+01  2.540e-03   5230.064  < 2e-16 ***
DESTIN_GRID_ID1908          1.262e+01  3.240e-03   3894.878  < 2e-16 ***
DESTIN_GRID_ID1909          1.300e+01  2.488e-03   5226.347  < 2e-16 ***
DESTIN_GRID_ID1912          9.915e+00  2.099e-02    472.375  < 2e-16 ***
DESTIN_GRID_ID1913          1.312e+01  2.159e-03   6075.988  < 2e-16 ***
DESTIN_GRID_ID1914          1.377e+01  1.957e-03   7037.752  < 2e-16 ***
DESTIN_GRID_ID1928          1.314e+01  2.975e-03   4418.232  < 2e-16 ***
DESTIN_GRID_ID1929          1.312e+01  3.094e-03   4239.862  < 2e-16 ***
DESTIN_GRID_ID1933          1.394e+01  2.046e-03   6813.321  < 2e-16 ***
DESTIN_GRID_ID1935          1.336e+01  2.490e-03   5366.527  < 2e-16 ***
DESTIN_GRID_ID1936          1.327e+01  2.426e-03   5470.274  < 2e-16 ***
DESTIN_GRID_ID1937          1.320e+01  2.495e-03   5291.584  < 2e-16 ***
DESTIN_GRID_ID1940          1.303e+01  2.368e-03   5503.461  < 2e-16 ***
DESTIN_GRID_ID1941          1.228e+01  3.321e-03   3697.295  < 2e-16 ***
DESTIN_GRID_ID1942          1.332e+01  4.578e-03   2909.865  < 2e-16 ***
DESTIN_GRID_ID1955          1.397e+01  2.070e-03   6746.485  < 2e-16 ***
DESTIN_GRID_ID1959          1.365e+01  2.115e-03   6456.775  < 2e-16 ***
DESTIN_GRID_ID1960          1.394e+01  1.857e-03   7509.190  < 2e-16 ***
DESTIN_GRID_ID1962          1.282e+01  2.633e-03   4866.846  < 2e-16 ***
DESTIN_GRID_ID1963          1.274e+01  2.484e-03   5127.783  < 2e-16 ***
DESTIN_GRID_ID1967          1.347e+01  2.164e-03   6221.395  < 2e-16 ***
DESTIN_GRID_ID1968          1.349e+01  2.573e-03   5240.905  < 2e-16 ***
DESTIN_GRID_ID1985          1.350e+01  2.699e-03   5004.128  < 2e-16 ***
DESTIN_GRID_ID1987          1.468e+01  1.631e-03   9001.949  < 2e-16 ***
DESTIN_GRID_ID1988          1.255e+01  2.800e-03   4481.503  < 2e-16 ***
DESTIN_GRID_ID1989          1.239e+01  3.192e-03   3881.483  < 2e-16 ***
DESTIN_GRID_ID1990          1.494e+01  1.583e-03   9437.214  < 2e-16 ***
DESTIN_GRID_ID1994          1.096e+01  1.249e-02    877.666  < 2e-16 ***
DESTIN_GRID_ID1995          1.295e+01  2.702e-03   4792.008  < 2e-16 ***
DESTIN_GRID_ID2010          1.363e+01  1.912e-03   7128.309  < 2e-16 ***
DESTIN_GRID_ID2011          1.366e+01  2.144e-03   6370.686  < 2e-16 ***
DESTIN_GRID_ID2012          1.285e+01  3.237e-03   3971.132  < 2e-16 ***
DESTIN_GRID_ID2013          1.300e+01  2.191e-03   5932.784  < 2e-16 ***
DESTIN_GRID_ID2014          1.313e+01  2.084e-03   6300.978  < 2e-16 ***
DESTIN_GRID_ID2015          1.354e+01  2.625e-03   5159.692  < 2e-16 ***
DESTIN_GRID_ID2016          1.313e+01  2.298e-03   5712.090  < 2e-16 ***
DESTIN_GRID_ID2017          1.318e+01  2.272e-03   5799.281  < 2e-16 ***
DESTIN_GRID_ID2021          1.164e+01  6.500e-03   1790.611  < 2e-16 ***
DESTIN_GRID_ID2038          1.431e+01  1.717e-03   8332.794  < 2e-16 ***
DESTIN_GRID_ID2039          1.277e+01  3.216e-03   3970.619  < 2e-16 ***
DESTIN_GRID_ID2040          1.302e+01  2.443e-03   5330.158  < 2e-16 ***
DESTIN_GRID_ID2041          1.375e+01  1.913e-03   7184.306  < 2e-16 ***
DESTIN_GRID_ID2042          1.274e+01  3.147e-03   4047.128  < 2e-16 ***
DESTIN_GRID_ID2043          1.353e+01  2.506e-03   5399.772  < 2e-16 ***
DESTIN_GRID_ID2044          1.342e+01  2.040e-03   6579.001  < 2e-16 ***
DESTIN_GRID_ID2064          1.340e+01  2.592e-03   5170.310  < 2e-16 ***
DESTIN_GRID_ID2065          1.319e+01  2.567e-03   5138.618  < 2e-16 ***
DESTIN_GRID_ID2066          1.325e+01  2.057e-03   6441.882  < 2e-16 ***
DESTIN_GRID_ID2067          1.261e+01  3.131e-03   4028.090  < 2e-16 ***
DESTIN_GRID_ID2068          1.306e+01  2.680e-03   4872.696  < 2e-16 ***
DESTIN_GRID_ID2070          1.355e+01  2.622e-03   5167.691  < 2e-16 ***
DESTIN_GRID_ID2071          1.362e+01  2.324e-03   5860.518  < 2e-16 ***
DESTIN_GRID_ID2093          1.358e+01  1.933e-03   7024.981  < 2e-16 ***
DESTIN_GRID_ID2094          1.348e+01  2.138e-03   6303.227  < 2e-16 ***
DESTIN_GRID_ID2095          1.344e+01  3.042e-03   4419.568  < 2e-16 ***
DESTIN_GRID_ID2098          1.328e+01  2.830e-03   4693.013  < 2e-16 ***
DESTIN_GRID_ID2119          1.332e+01  2.533e-03   5258.955  < 2e-16 ***
DESTIN_GRID_ID2120          1.400e+01  2.036e-03   6878.664  < 2e-16 ***
DESTIN_GRID_ID2123          1.243e+01  3.320e-03   3745.246  < 2e-16 ***
DESTIN_GRID_ID2147          1.354e+01  2.075e-03   6526.366  < 2e-16 ***
DESTIN_GRID_ID2148          1.330e+01  2.151e-03   6179.955  < 2e-16 ***
DESTIN_GRID_ID2149          1.381e+01  2.358e-03   5856.055  < 2e-16 ***
DESTIN_GRID_ID2150          1.157e+01  5.985e-03   1932.407  < 2e-16 ***
DESTIN_GRID_ID2151          1.172e+01  5.189e-03   2257.878  < 2e-16 ***
DESTIN_GRID_ID2152          1.411e+01  1.975e-03   7141.937  < 2e-16 ***
DESTIN_GRID_ID2154          1.199e+01  4.649e-03   2579.305  < 2e-16 ***
DESTIN_GRID_ID2174          1.190e+01  4.821e-03   2468.063  < 2e-16 ***
DESTIN_GRID_ID2177          1.526e+01  1.543e-03   9894.495  < 2e-16 ***
DESTIN_GRID_ID2178          1.230e+01  2.835e-03   4339.635  < 2e-16 ***
DESTIN_GRID_ID2179          1.361e+01  2.141e-03   6355.825  < 2e-16 ***
DESTIN_GRID_ID2180          1.262e+01  3.642e-03   3465.759  < 2e-16 ***
DESTIN_GRID_ID2201          1.321e+01  2.430e-03   5435.794  < 2e-16 ***
DESTIN_GRID_ID2203          1.309e+01  3.591e-03   3645.617  < 2e-16 ***
DESTIN_GRID_ID2204          1.343e+01  2.451e-03   5480.509  < 2e-16 ***
DESTIN_GRID_ID2205          1.275e+01  2.406e-03   5298.798  < 2e-16 ***
DESTIN_GRID_ID2206          1.367e+01  1.862e-03   7339.591  < 2e-16 ***
DESTIN_GRID_ID2208          1.312e+01  2.637e-03   4976.080  < 2e-16 ***
DESTIN_GRID_ID2228          1.288e+01  2.696e-03   4778.998  < 2e-16 ***
DESTIN_GRID_ID2231          1.304e+01  2.367e-03   5507.827  < 2e-16 ***
DESTIN_GRID_ID2233          1.360e+01  1.827e-03   7446.190  < 2e-16 ***
DESTIN_GRID_ID2234          7.493e+00  9.130e-02     82.067  < 2e-16 ***
DESTIN_GRID_ID2235          1.062e+01  3.132e-02    339.076  < 2e-16 ***
DESTIN_GRID_ID2254          1.328e+01  5.670e-03   2342.603  < 2e-16 ***
DESTIN_GRID_ID2255          1.261e+01  4.082e-03   3088.299  < 2e-16 ***
DESTIN_GRID_ID2256          1.298e+01  2.576e-03   5037.797  < 2e-16 ***
DESTIN_GRID_ID2257          1.279e+01  7.745e-03   1650.855  < 2e-16 ***
DESTIN_GRID_ID2259          1.225e+01  4.370e-03   2803.355  < 2e-16 ***
DESTIN_GRID_ID2260          1.284e+01  2.293e-03   5599.372  < 2e-16 ***
DESTIN_GRID_ID2261          1.287e+01  2.291e-03   5618.681  < 2e-16 ***
DESTIN_GRID_ID2262          1.188e+01  4.894e-03   2426.809  < 2e-16 ***
DESTIN_GRID_ID2281          1.279e+01  3.945e-03   3242.679  < 2e-16 ***
DESTIN_GRID_ID2282          1.401e+01  1.933e-03   7247.351  < 2e-16 ***
DESTIN_GRID_ID2283          1.278e+01  2.713e-03   4711.014  < 2e-16 ***
DESTIN_GRID_ID2285          1.354e+01  2.192e-03   6177.751  < 2e-16 ***
DESTIN_GRID_ID2286          1.269e+01  2.765e-03   4588.446  < 2e-16 ***
DESTIN_GRID_ID2287          1.365e+01  1.722e-03   7923.269  < 2e-16 ***
DESTIN_GRID_ID2288          1.124e+01  6.842e-03   1642.974  < 2e-16 ***
DESTIN_GRID_ID2310          1.331e+01  2.212e-03   6018.221  < 2e-16 ***
DESTIN_GRID_ID2312          1.229e+01  5.091e-03   2413.349  < 2e-16 ***
DESTIN_GRID_ID2313          1.446e+01  1.722e-03   8399.148  < 2e-16 ***
DESTIN_GRID_ID2314          1.449e+01  1.588e-03   9122.015  < 2e-16 ***
DESTIN_GRID_ID2315          1.251e+01  2.674e-03   4677.491  < 2e-16 ***
DESTIN_GRID_ID2316          1.319e+01  2.032e-03   6489.472  < 2e-16 ***
DESTIN_GRID_ID2335          1.165e+01  1.356e-02    859.423  < 2e-16 ***
DESTIN_GRID_ID2339          1.334e+01  2.587e-03   5156.543  < 2e-16 ***
DESTIN_GRID_ID2340          1.319e+01  1.936e-03   6812.909  < 2e-16 ***
DESTIN_GRID_ID2341          1.354e+01  1.771e-03   7647.760  < 2e-16 ***
DESTIN_GRID_ID2342          1.237e+01  2.425e-03   5100.919  < 2e-16 ***
DESTIN_GRID_ID2343          1.221e+01  3.844e-03   3176.571  < 2e-16 ***
DESTIN_GRID_ID2363          1.247e+01  3.875e-03   3217.248  < 2e-16 ***
DESTIN_GRID_ID2367          1.299e+01  3.195e-03   4064.877  < 2e-16 ***
DESTIN_GRID_ID2368          1.311e+01  2.280e-03   5750.810  < 2e-16 ***
DESTIN_GRID_ID2369          1.391e+01  1.854e-03   7502.854  < 2e-16 ***
DESTIN_GRID_ID2370          1.478e+01  1.612e-03   9168.867  < 2e-16 ***
DESTIN_GRID_ID2371          1.275e+01  2.624e-03   4856.695  < 2e-16 ***
DESTIN_GRID_ID2390          1.401e+01  1.977e-03   7086.062  < 2e-16 ***
DESTIN_GRID_ID2391          1.379e+01  2.107e-03   6546.924  < 2e-16 ***
DESTIN_GRID_ID2394          1.153e+01  5.931e-03   1943.476  < 2e-16 ***
DESTIN_GRID_ID2395          1.297e+01  2.171e-03   5974.919  < 2e-16 ***
DESTIN_GRID_ID2396          1.306e+01  1.932e-03   6758.234  < 2e-16 ***
DESTIN_GRID_ID2397          1.155e+01  5.587e-03   2067.078  < 2e-16 ***
DESTIN_GRID_ID2398          1.232e+01  3.731e-03   3302.731  < 2e-16 ***
DESTIN_GRID_ID2418          1.325e+01  2.861e-03   4631.991  < 2e-16 ***
DESTIN_GRID_ID2419          1.383e+01  2.383e-03   5804.927  < 2e-16 ***
DESTIN_GRID_ID2422          1.174e+01  9.127e-03   1286.063  < 2e-16 ***
DESTIN_GRID_ID2423          1.214e+01  3.490e-03   3478.421  < 2e-16 ***
DESTIN_GRID_ID2424          1.348e+01  1.906e-03   7072.429  < 2e-16 ***
DESTIN_GRID_ID2425          1.474e+01  1.678e-03   8786.830  < 2e-16 ***
DESTIN_GRID_ID2426          1.285e+01  4.416e-03   2911.140  < 2e-16 ***
DESTIN_GRID_ID2443          1.404e+01  1.968e-03   7131.944  < 2e-16 ***
DESTIN_GRID_ID2445          1.361e+01  2.121e-03   6417.332  < 2e-16 ***
DESTIN_GRID_ID2449          1.198e+01  6.127e-03   1955.922  < 2e-16 ***
DESTIN_GRID_ID2450          1.241e+01  2.748e-03   4515.385  < 2e-16 ***
DESTIN_GRID_ID2451          1.374e+01  1.784e-03   7702.157  < 2e-16 ***
DESTIN_GRID_ID2472          1.109e+01  1.621e-02    684.189  < 2e-16 ***
DESTIN_GRID_ID2473          1.380e+01  2.410e-03   5725.674  < 2e-16 ***
DESTIN_GRID_ID2478          1.265e+01  2.762e-03   4579.292  < 2e-16 ***
DESTIN_GRID_ID2479          1.177e+01  7.755e-03   1517.398  < 2e-16 ***
DESTIN_GRID_ID2497          1.334e+01  2.433e-03   5480.998  < 2e-16 ***
DESTIN_GRID_ID2499          1.268e+01  3.849e-03   3293.882  < 2e-16 ***
DESTIN_GRID_ID2505          1.294e+01  2.931e-03   4414.657  < 2e-16 ***
DESTIN_GRID_ID2527          1.414e+01  1.931e-03   7323.271  < 2e-16 ***
DESTIN_GRID_ID2532          1.201e+01  4.336e-03   2769.321  < 2e-16 ***
DESTIN_GRID_ID2533          1.193e+01  6.452e-03   1849.749  < 2e-16 ***
DESTIN_GRID_ID2551          1.322e+01  3.627e-03   3645.988  < 2e-16 ***
DESTIN_GRID_ID2553          1.249e+01  5.669e-03   2203.156  < 2e-16 ***
DESTIN_GRID_ID2554          1.174e+01  7.151e-03   1641.167  < 2e-16 ***
DESTIN_GRID_ID2559          1.203e+01  5.798e-03   2074.526  < 2e-16 ***
DESTIN_GRID_ID2580          1.351e+01  2.380e-03   5674.739  < 2e-16 ***
DESTIN_GRID_ID2581          1.242e+01  5.042e-03   2462.162  < 2e-16 ***
DESTIN_GRID_ID2607          1.308e+01  2.506e-03   5220.383  < 2e-16 ***
DESTIN_GRID_ID2608          1.208e+01  5.473e-03   2207.914  < 2e-16 ***
DESTIN_GRID_ID2634          1.514e+01  1.634e-03   9265.326  < 2e-16 ***
DESTIN_GRID_ID2635          1.253e+01  3.631e-03   3450.888  < 2e-16 ***
DESTIN_GRID_ID2636          1.338e+01  2.534e-03   5279.442  < 2e-16 ***
DESTIN_GRID_ID2661          1.299e+01  2.336e-03   5561.023  < 2e-16 ***
DESTIN_GRID_ID2663          1.361e+01  1.916e-03   7099.130  < 2e-16 ***
DESTIN_GRID_ID2665          1.400e+01  2.126e-03   6588.104  < 2e-16 ***
DESTIN_GRID_ID2688          1.315e+01  2.619e-03   5022.265  < 2e-16 ***
DESTIN_GRID_ID2689          1.388e+01  2.002e-03   6933.344  < 2e-16 ***
DESTIN_GRID_ID2690          1.349e+01  2.137e-03   6314.449  < 2e-16 ***
DESTIN_GRID_ID2691          1.315e+01  2.144e-03   6135.127  < 2e-16 ***
DESTIN_GRID_ID2693          1.356e+01  2.361e-03   5742.934  < 2e-16 ***
DESTIN_GRID_ID2715          1.307e+01  2.890e-03   4522.003  < 2e-16 ***
DESTIN_GRID_ID2717          1.324e+01  1.926e-03   6875.847  < 2e-16 ***
DESTIN_GRID_ID2718          1.228e+01  3.952e-03   3108.148  < 2e-16 ***
DESTIN_GRID_ID2719          1.341e+01  2.055e-03   6526.801  < 2e-16 ***
DESTIN_GRID_ID2742          1.333e+01  2.510e-03   5310.338  < 2e-16 ***
DESTIN_GRID_ID2743          1.319e+01  3.674e-03   3590.737  < 2e-16 ***
DESTIN_GRID_ID2744          1.376e+01  1.947e-03   7065.120  < 2e-16 ***
DESTIN_GRID_ID2745          1.353e+01  1.960e-03   6906.809  < 2e-16 ***
DESTIN_GRID_ID2747          1.269e+01  3.167e-03   4007.603  < 2e-16 ***
DESTIN_GRID_ID2768          1.334e+01  2.657e-03   5022.508  < 2e-16 ***
DESTIN_GRID_ID2771          1.516e+01  1.600e-03   9476.203  < 2e-16 ***
DESTIN_GRID_ID2773          1.259e+01  2.752e-03   4574.558  < 2e-16 ***
DESTIN_GRID_ID2798          1.189e+01  4.430e-03   2683.989  < 2e-16 ***
DESTIN_GRID_ID2799          1.281e+01  2.341e-03   5471.354  < 2e-16 ***
DESTIN_GRID_ID2800          1.444e+01  1.713e-03   8431.470  < 2e-16 ***
DESTIN_GRID_ID2824          1.422e+01  1.998e-03   7118.165  < 2e-16 ***
DESTIN_GRID_ID2825          1.319e+01  2.001e-03   6591.632  < 2e-16 ***
DESTIN_GRID_ID2826          1.257e+01  3.370e-03   3731.409  < 2e-16 ***
DESTIN_GRID_ID2827          1.502e+01  1.631e-03   9209.383  < 2e-16 ***
DESTIN_GRID_ID2852          1.271e+01  3.248e-03   3914.876  < 2e-16 ***
DESTIN_GRID_ID2853          1.417e+01  1.661e-03   8528.998  < 2e-16 ***
DESTIN_GRID_ID2854          1.353e+01  2.084e-03   6493.238  < 2e-16 ***
DESTIN_GRID_ID2878          1.283e+01  3.169e-03   4049.196  < 2e-16 ***
DESTIN_GRID_ID2879          1.292e+01  2.502e-03   5164.768  < 2e-16 ***
DESTIN_GRID_ID2880          1.235e+01  3.141e-03   3930.684  < 2e-16 ***
DESTIN_GRID_ID2881          1.330e+01  2.724e-03   4883.625  < 2e-16 ***
DESTIN_GRID_ID2907          1.231e+01  4.173e-03   2949.073  < 2e-16 ***
DESTIN_GRID_ID2908          1.360e+01  2.182e-03   6231.668  < 2e-16 ***
DESTIN_GRID_ID2933          1.432e+01  2.758e-03   5192.889  < 2e-16 ***
DESTIN_GRID_ID2934          1.275e+01  3.021e-03   4219.398  < 2e-16 ***
DESTIN_GRID_ID3098          1.379e+01  3.413e-03   4038.752  < 2e-16 ***
log(TORIGIN_BIZ_COUNT)     -5.619e-03  9.849e-05    -57.053  < 2e-16 ***
log(TORIGIN_FINSERV_COUNT)  6.986e-02  8.982e-05    777.770  < 2e-16 ***
log(TORIGIN_MRTEXIT_COUNT)  5.929e-02  1.611e-04    368.131  < 2e-16 ***
log(TORIGIN_BUSSTOP_COUNT)  2.170e-01  2.489e-04    871.871  < 2e-16 ***
log(TORIGIN_HDBCOMM_UNITS) -1.469e-04  5.435e-05     -2.702  0.00689 ** 
log(TORIGIN_HDBRES_UNITS)   4.258e-01  1.617e-04   2633.529  < 2e-16 ***
log(TORIGIN_SCHOOLS_COUNT)  1.248e-01  2.220e-04    562.244  < 2e-16 ***
log(DISTANCE)              -1.378e+00  1.216e-04 -11335.668  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2876477793  on 101668  degrees of freedom
Residual deviance:  138440291  on 101312  degrees of freedom
AIC: 139198612

Number of Fisher Scoring iterations: 6
CalcRSquared(decSIM_Poisson4$data$TRIPS, decSIM_Poisson4$fitted.values)
[1] 0.5698026
model_list4 <- list(originConstrained4=orcSIM_Poisson4,
                   destinationConstrained4=decSIM_Poisson4,
                   doublyConstrained2=dbcSIM_Poisson2)
compare_performance(model_list4,
                    metrics = "RMSE")
# Comparison of Model Performance Indices

Name                    | Model |     RMSE
------------------------------------------
originConstrained4      |   glm | 3001.307
destinationConstrained4 |   glm | 3188.985
doublyConstrained2      |   glm | 2302.478

8.2 Final Model

9 Conclusion and Future Work